. One priority for avoiding runaway climate change is finding viable alternatives to mechanical air-conditioning. Recent advances in daytime radiative cooling materials are promising. However, researchers have not yet shown how to use them for passive cooling below ambient temperature indoors. Ventilation is challenging in this regard as healthy air changes will heat the sub-ambient interior. We present a field study using analog models to observe how daytime radiative cooling materials can passively reject heat from inside naturally ventilated buildings. We mounted two test boxes on a rooftop in Southern California, replicating in miniature the thermal loads, losses, and air changes for one occupant. The control box represented a reference ‘gold standard’ for passive cooling: internal thermal mass with night ventilation. The test box had an uninsulated metal roof with a top surface for daytime radiative cooling. Both boxes had internal heat sources with ventilation driven not by wind but by buoyancy. Under clear skies, the test box maintained an interior temperature of 3.9 +/- 4.8 °C below the mean prevailing exterior temperature while venting 6.9 +/- 0.3 air changes per hour during the day. In comparison, the control box maintained an interior temperature of 5.0 +/- 1.7 °C above the mean prevailing exterior temperature while venting 8.6 +/- 0.1 air changes per hour during the night. We show with a calibrated model how to improve the sub-ambient temperature stability of the test box with more thermal mass in the roof and how to scale up the results to actual buildings. Significance Statement. In a warming world, new passive cooling techniques could help curtail the growing demand for mechanical air-conditioning and the resulting emissions that further heat the planet. Recent breakthroughs in passive radiative cooling materials, which reflect sunshine while emitting infrared heat into cold outer space, show promise. But it’s unclear how these materials could replace mechanical heat rejection in well-ventilated buildings. In a field experiment with two model buildings, each scaled to one person's heat load and fresh air needs, we show how to chill the air below the ambient temperature inside a naturally ventilated enclosure by coupling terrestrial radiation, thermal mass, and gravity-driven air changes, while outperforming a reference 'gold standard' for passive cooling. Keywords: Radiative cooling. Natural ventilation. Thermal comfort. Energy efficiency. Fortin et al. (2023) Cool running 2 Introduction Climate change is driving demand for mechanical air-conditioning while the growing greenhouse gas emissions from using and making these systems, not least from leaking refrigerants (1), further heat the planet (2, 3). Several breakthroughs in passive radiative cooling materials, which reflect sunshine like a mirror while emitting infrared heat into cold outer space through the atmospheric window, have been made recently (4–11). However, if these materials can augment or replace mechanical heat rejection in buildings (12–16), it is unclear how and where or for which occupancy types, especially now that healthy ventilation with plentiful air changes is a priority (17). With some success, daytime radiative cooling materials and coatings have been added to the outside of insulated roofs (14–16, 18), improving the energy efficiency of entire building stocks. However, true cooling entails removing heat, which is more challenging than improving protection from overheating. On a hot day, these surface treatments can only reduce the temperature difference across the exterior insulation, rejecting little to no heat from the interior. Some researchers, including Felix Trombe, often cited as the first pioneer of radiative cooling, have explored removing insulation from sky-facing surfaces to reject heat from the interior (Figure 1A to C) (15, 19–22). While these test enclosures produced sub-ambient temperatures, the need for ventilation, and its effect on the heat balance, seems to be a crucial oversight in the experiments. Not all buildings are mechanically ventilated and air-conditioned, particularly in developing countries. The current ‘gold standard’ for passive cooling in hot and dry climates (assuming water is too precious to evaporate as a spray (23)) is an internal thermal mass with night ventilation (24–27). The thermal mass, protected by external insulation, absorbs internal heat from people, devices, lighting, and so on, while the ventilation lets the mass discharge this heat at night. Even simpler, the ventilation may be driven naturally by a combination of wind and buoyancy forces (28–30). In this study, we examine how to surpass this ‘gold standard’ for passive cooling by adding 24-hour radiative cooling from an uninsulated roof. We experimentally demonstrate a model enclosure that maintained an interior temperature of 3.9°C below the mean prevailing exterior temperature while consistently venting nearly 7 air changes per hour during the day. Our results demonstrate that it is in fact possible to passively maintain structures in the built environment cooler than their ambient using passive radiative cooling while also ensuring adequate ventilation from the exterior. Heat balance For this purpose, we define the evolution of the air temperature inside a ventilated enclosure as 𝜌𝐶𝑝!" 𝑉!" 𝑑𝑇!"𝑑𝑡=𝑊#+𝑊$+𝑊%+𝑊&+𝑊' ( 1 ) where 𝜌𝐶𝑝!" is the volumetric heat capacity of the air, 𝑉!" is the volume of interior air, 𝑊#, 𝑊$ and 𝑊% are the internal heat exchanges with the ventilation, thermal mass, and the underside of the roof, respectively, 𝑊& is the heat transfer through the insulated external walls, and 𝑊' is the internal heat generated by people, devices, and so on. Not only do we wish to put the interior space in radiant communication with outer space via the roof, but we also want to put the interior air in fluid communication with the atmosphere. In the heat balance of Eq. 1, ventilation (𝑊#) heats or cools the interior depending on its sign (i.e., the relative temperature of the exterior). Ventilation is necessary for health reasons, as the COVID-19 pandemic has highlighted. We wish to understand how to achieve passive cooling to sub-ambient indoor temperatures without sacrificing healthy air changes. The geographical limits and practical applications may be evaluated once this physical balance is understood. Fortin et al. (2023) Cool running 3 Figure 1. Passive radiative cooling in unventilated and ventilated enclosures. (A) North-East view showing the radiative cooling façade of the cold house designed and built by Felix Trombe and his team in 1963-63 in Odeillo, France (21). (B) View of an experimental cooling container used by Trombe and his team in Mont-Louis, France, undated (22). (C) Diagrammatic vertical section of Trombe’s patented design for the cold house, 1967 (19). (D) Schematic drawing of our experimental box showing how the water bottles can be replaced by an equivalent concrete thermal mass. (E) Schema of the proportions required for the thermal mass, radiator, and ventilation openings to match the thermal loads, losses, and air changes attributable to one occupant (F) Schematic section and axonometric view of an architectural concept for a 10-people building. The driving force for buoyancy ventilation can be formulated as a ‘reduced gravity,’ 𝑔′=𝑔𝛽𝛥𝑇, where 𝑔 is the gravitational acceleration, 𝛽 is the coefficient of thermal expansion of air, and 𝛥𝑇=𝑇(−𝑇!" is the difference between ambient and indoor air temperature. The heat exchanges from the ventilation 𝑊# is then calculated from the natural ventilation flow rate 𝑄 as 𝑄=𝐴∗ 34𝛥𝑝𝑤 −𝑔′𝐻𝜌4 ( 2 ) 𝑊#=𝜌𝐶𝑝!"𝛥𝑇 𝑄 ( 3 ) where A* is the effective size of the ventilation openings, 𝛥𝑝𝑤 is the wind pressure difference between the openings, H is the height between the openings, and 𝜌 is the air density. Wind and buoyancy forces may complement or compete with each other, depending on the vent locations and their orientation to the wind. Later, we design the vents to eliminate the influence of wind. In any case, we model the internal thermal mass as lumped, that is, neglecting the diffusion of heat through the mass, to simplify the thermal coupling with buoyancy ventilation Fortin et al. (2023) Cool running 4 𝜌𝐶𝑝$ 𝑉$ 𝑑𝑇$𝑑𝑡= −𝑊$ ( 4 ) 𝑊$=𝑆$ ℎ $(𝑇$−𝑇!") ( 5 ) where 𝑇$ is the mass temperature, 𝜌𝐶𝑝$ is the heat capacity of the thermal mass, 𝑉$ is the thermal mass volume, 𝑆$ is the surface area in contact with the indoor air, and ℎ$ the heat transfer coefficient to and from the surface of the thermal mass which is in contact with the interior air. We also model the thermal mass in the roof-radiator as a lumped mass 𝜌𝐶𝑝% 𝑉%𝑑𝑇%𝑑𝑡= 𝑊*+,−𝑊% ( 6 ) 𝑊% =𝑆% ℎ %(𝑇%−𝑇!") ( 7 ) where the subscript 𝑅 indicates the equivalent parameters for the radiator as for the thermal mass in Eq. 4 and 5, and 𝑊*+, is the balance of thermal radiation, solar radiation, and convection on the top surface of the radiator, defined below. We now report our experiment, investigating the coupling of thermal mass, buoyancy ventilation, and radiative cooling in passive building design. We show how to maintain sub-ambient interior temperatures while producing steady air changes, with results that scale to per-person heat loads and fresh air requirements. Results We installed two insulated boxes in a warm, dry climate (Topanga Valley, CA) with an open view of the sky (Figure 2). The first box, hereafter called the control box, had an internal thermal mass, an internal heat source, and two upward-pointing ventilation stacks. In this box, ventilation only occurred when the buoyancy pressure was negative, that is, when the interior temperature was warmer than the exterior, prompting upward flow through the shortest pipe-vent (Figure 2A and C). The other box, hereafter called the test box, had the same thermal mass and internal heat source, but the roof was an uninsulated aluminum plate with a daytime radiative cooling material glued to its top surface (Materials and Methods). The underside (soffit) of the radiator was directly coupled to the interior by natural convection. Its sky-facing side had an infrared-transparent guard above it to limit convective heating from the exterior. In the test box, the ventilation stacks pointed downward so as not to interfere with the radiator. As a result, the ventilation was only triggered when the interior temperature was cooler than the exterior. As such, the ventilation of both boxes was driven by the temperature difference between inside and outside, but for opposite signs, biasing the control box for night venting and the test box for day venting. In this way, both boxes could reach their lowest temperatures while still providing a healthy rate of ventilation for half a daily cycle. We scaled the experiment targeting a flow rate of ~0.1 l/s (liters/second), representing 1% of the ventilation rate that is required by one person. (Engineering guidelines recommend 10 l/s per person in non-residential buildings, although these rates are likely to increase to 14 l/s following the COVID-19 pandemic (17).) Meanwhile, the differential height of the pipe-vents helped to drive the buoyancy flow, promote good mixing of the interior air by the incoming plume, and ensure unidirectional flow through each pipe-vent for measurement purposes (30). The closeness of the pipes to each other, and the fact they hardly protruded outside the box (as shown in Figure 2A to D) helped to eliminate differential wind pressure (25, 31). Fortin et al. (2023) Cool running 5 Figure 2. (A) Control box at night. Upward mixing ventilation when the interior is warmer than the exterior. (B) Test box at night. No ventilation when the interior is warmer than the exterior. (C) Control box during day. No ventilation when the interior is cooler than the exterior. (D) Test box during day. Downward mixing ventilation when the interior is cooler than the exterior. (E) Nomenclature (F) Photo of the experiment setup in Southern California. (G) Annotated photo of the interior of the test box. (G) Annotated photo showing the radiator on top of the test box (front) and the high-level pipe-vents of the control box (back). The thermal mass inside each test box was a set of water bottles, chosen for cost, simplicity, and volumetric heat capacity. The thermal mass, ventilation flow rate, and roof radiator were sized so that all the heat exchanges with the interior (listed in Eq. 1) were reduced by the same order of magnitude, representing approximately one percent of the heat load and ventilation requirements typically associated with one occupant. Since ventilation exchanges were potentially the most challenging to get right, we started with Eq. 2, sizing the cross-sectional area and length of the pipe-vents to achieve a flow rate of ∽0.1 liter/sec (the equivalent of 10 liter/sec. at building scale), assuming no wind and a 5 °C temperature difference with the exterior. Then, we calculated the radiative cooling roof area (𝑆%) needed to offset an internal heat source of 1.2 W (or 120 W) based on simulations for 𝑊*+, and the properties of the daytime radiative cooling material (described in Materials and Methods). In parallel, we used thermal mass scaling rules as a starting point to determine the surface area (𝑆$) and volume (𝑉$) of internal mass that would be needed to keep the interior temperature within a ∽5 °C range under an exterior temperature swing of ∽15 °C (26). Finally, we input those values into our theoretical model (Eq. 1 to 7) and proceeded by iteration to find the combination that would be both practical and produce the coldest and most stable interior temperature. Fortin et al. (2023) Cool running 6 Figure 3. Temperature, ventilation flow and heat exchange measurements. (A) Air temperature Tin inside the control and test boxes with ambient temperature Ta for two typical days in September 2022, when the mean prevailing ambient temperature Tpm was 21.9 °C, with an average of 23.7 °C between the daily maximum and minimum Ta. (B) Typical variations of Tin and Ta for two days in November 2022, after 1.5 times more thermal mass added in both boxes. Tpm was 9.4 °C, and the difference between the daily maximum and minimum Ta was 22.4 °C. The interior of the control and test boxes varied on average 5.0 +/- 1.7 °C above and 3.9 +/- 4.8 °C. (C) Comparison of the ventilation flow rate Q and the number of air changes per hour in the control and test boxes for two typical days in September and November 2022. Since Tin is more stable in November, the temperature difference between Ta and Tin increases, and so does the ventilation rate. (D) Normalized heat exchanges inside the control box during two typical days in November 2022 (scaled to WH = 1.2 W). (E) Normalized heat exchanges inside the test box during two days in November 2022 (scaled to WH = 1.2 W). Note the change in x-axis scale (F) Comparison of the distribution of the ventilation flow rate Q and the number of air changes per hour during the 7-day and 14-day experiments in September and November 2022. (G) Radiator temperature TR with the ambient air temperature Ta, indoor air temperature Tin, air temperature inside the convection guard Tcg, and effective sky temperature Tsky for two typical days in November 2022. (H) Measured heat fluxes on the top surface (Wsky/SR) and soffit (WR/SR) of the radiator, with downward solar radiation flux Psun, net atmospheric radiation flux for a blackbody at ambient temperature 𝑃!"#,%%, and predicted parasitic losses through the convection guard 𝑃&'(( for two typical days in November 2022 and from 5 AM to 7 PM on November 20. Temperature and flow rate We ran two experiments under clear sky conditions and measured the air temperature and ventilation exchanges inside the boxes, as well as the other heat exchanges expressed in Eq. 1. During the first experiment in September, the interior temperature of the control box fluctuated 4.3 +/- 2.5 °C above the mean prevailing ambient temperature 𝑇-. (Figure 3A). (Note that the error reported here represents the difference between the mean daily maximum and minimum temperatures). In comparison, the test box remained 1.6 +/- 6.8 °C below 𝑇-. (Figure 3A). The Fortin et al. (2023) Cool running 7 interior temperature of the test box was less stable than the control box, and its peak temperature occasionally exceeded that of the control, so we decided to add 1.5 times more thermal mass in the boxes to further stabilize their interior temperature in a second experiment. This took place in November, and the interior of the control box fluctuated 5.0 +/- 1.7 °C above 𝑇-. while the extra mass helped dampen the interior temperature swing (𝑇!",.(0−𝑇!",.!") by factor 0.86 relative to the exterior. The test box varied on average 3.9 +/- 4.8 °C below 𝑇-. and reduced the ambient temperature swing (𝑇(,.(0−𝑇(,.!") by a factor of 0.59 (Figure 3B). The relative instability of the test box was caused by the variation in the radiator temperature since the test box had the same amount of internal thermal mass as the control box. The ventilation stacks in both boxes were designed to produce unidirectional, wind-insensitive ventilation and well-mixed thermal conditions inside the boxes (Materials and Methods). As intended, the ventilation did occur over half-day cycles based on the temperature difference between the inside and outside (Figure 3C and 3F). In September, the control box vented on average 0.133 +/- 0.015 l/s during the day, and the test box vented 0.061 +/- 0.013 l/s during the night. (Note that the error reported here represents the reading error from the sensors, which was greater than the standard deviation.) In comparison, the control box vented 0.143 +/- 0.015 l/s during the day, and the test box vented 0.115 +/- 0.014 l/s during the night in November. Since the air temperature was more stable inside the control box, it led to a bigger temperature difference with the outside and larger ventilation flow rates. Similarly, the temperature variations in the control and test boxes were dampened by the additional thermal mass in November and therefore produced more ventilation. Interior heat balance Along with the temperature and ventilation flow measurements, we measured all the components of the heat balance in Eq. 1 (Materials and Methods). In the control box, the internal thermal mass produced alternating heating and cooling cycles (𝑊$), depending on whether it was warmer or cooler than the interior (Figure 3D). Because the ventilation only occurred when the inside of the box was warmer than the ambient air, the thermal mass cooled down at night faster than it warmed up during the day, biasing the system towards cooler temperatures. In the test box, the heat absorbed by the thermal mass from ventilation changes during the day was discharged by the radiator at night, through a combination of convection and radiation, or just radiation, depending on the temperature of the radiator. However, the roof thermal mass did overheat (𝑊% > 0) in the afternoon when the solar loads were particularly strong, and when the interior temperature was at its coolest relative to the ambient (Figure 3E). At these times, the internal thermal mass (𝑊$) absorbed most of the heat brought in by ventilation, and the thermal inertia of the indoor air cooled the roof (𝑊%), not the other way around. Radiator fluxes While the interior cooling power of the radiator was on average 1.9 times more than the heating power from the heat source, this cooling was somewhat inconsistent (Figure 3E). As a result, the internal thermal mass would cool down at night faster in the test box than in the control box, but it also warmed up faster during the day, so its stabilizing effect was limited. In this regard, it is important to understand how to potentially stabilize the roof temperature, which is not obvious with conjugate heat exchanges occurring simultaneously on both sides (Eq. 6). The balance of the radiation and convection fluxes at the top surface of the radiator (𝑊*+,) may be calculated from the effective sky temperature 𝑇*+, as Fortin et al. (2023) Cool running 8 𝑇*+,=(𝑇(1 −𝑃"23,44𝜎56)6/1 ( 8 ) 𝑊*+,=𝑆% (𝜖 𝜎 (𝑇%1−𝑇*+,1)− 𝛼 𝑃*8"−𝑃9:**) ( 9 ) where 𝜖 is the hemispherical emissivity of the roof surface (Materials and Methods), 𝑃"23,44 is the net atmospheric radiation flux for a blackbody at ambient temperature, 𝛼 𝑃*8" is the absorbed solar radiation flux based on the surface’s solar absorptivity 𝛼 (Materials and Methods), and 𝑃9:** is the sum of parasitic losses to the environment, including convection and re-radiation from the convection guard. In the November experiment, the radiator temperature (𝑇%) followed the ambient temperature (Ta), but remained on average 6.4 °C and 3.7 °C cooler under peak solar irradiance and during the night, respectively (Figure 3G). Even though 𝑇% stayed below the ambient temperature throughout the experiment, it followed the ambient temperature closely, causing it to overshoot the indoor air by up to 9.5 °C in the afternoon. This instability was not helped by overheating inside the convection guard (Tcg > Ta), which exceeded the ambient temperature by up to 4°C in the afternoon, adding unnecessary heat to the radiator (see 𝑃9:** in Figure 3H). Interior temperature stability To further analyze the sub-ambient temperatures inside the experiment boxes, and understand if they could have evolved with more stability, it is useful to normalize the interior temperature as 𝜃=(𝑇−𝑇0)/𝛥𝑇( ( 10 ) where 𝑇0=(𝑇(,.(0+𝑇(,.!")/2, is the daily mean ambient temperature and 𝛥𝑇(=E𝑇(,.(0−𝑇0E is the daily ambient temperature increment above the mean. In Figure 4, we compare these temperatures with the prevailing mean ambient temperature, which serves as a reference in the ASHRAE adaptive comfort standard for naturally ventilated buildings (32). This design standard reflects empirical evidence that peoples’ thermal expectations change with the predominant weather and allows a 5-7°C range of acceptable indoor temperatures (33, 34). The upper and lower limits to keep at least 80% of the occupants comfortable are 𝑇:-,.!"=14.3 + 0.31 𝑇-. ( 11 ) 𝑇:-,.(0=21.3 + 0.31 𝑇-. ( 12 ) where 𝑇:-, is the indoor operative temperature (a composite of the radiant and air temperature), and 𝑇-. is the prevailing mean ambient temperature (defined as the average of the daily mean outdoor temperature for a sequence of 7 to 30 days (32)). It’s worth noting that in the range 20.7 °C < 𝑇-. < 30.9 °C, an interior temperature equal to the prevailing mean is comfortable. Above this threshold (𝑇-. > 30.9 °C), the interior space needs to be cooled below the prevailing mean, working against daytime ventilation (𝑊#), which will act as a heat gain. Fortin et al. (2023) Cool running 9 Figure 4. Interior temperature stability and prediction for a massive roof radiator. (A) Daily mean, max and mean temperatures inside the control (yellow) and test box (green), with the effective sky temperature (Tsky, Eq. 8) from November 12 to 26 2022. All temperatures are normalized based on relative to the ambient temperature using Eq. 10. The width of each band indicates the daily max. and min. temperature. The two dashed gray lines are the prevailing mean ambient temperature ϴpm, and the normalized lower limit for adaptive comfort ϴop,min when Tpm = 30.9 °C and ϴpm = ϴop,max. (B) Predictions from our calibrated model showing the interior temperature of the test box (green) with a twenty-fold increase in the roof’s thermal mass. (C) Influence of the roof’s mass increase on the mean, max. and min. temperatures inside the test box. (D) Distribution of Tin and Ta from November 12 to 26, 2022. (E) Distribution of the normalized temperature inside the control (yellow) and test (light green) boxes with ambient temperature ϴa and the hypothetical scenario with more thermal mass in the roof (green). (F) Influence of the relative cooling (𝑊)+𝑊*)/𝑊+ on the daily mean temperature and ventilation flow rate inside the control (yellow) and test (green) boxes. Normalizations defined in text. As Figure 4A shows, the mean temperature in the test box stayed below the prevailing mean (𝜃-.) for the 14 days during the November experiment, while the control box stayed above this threshold. (Note that, while 𝑇-. is a constant, 𝜃-. varies slightly day to day in Figure 4A and B because it is normalized for daily values of 𝑇0 and 𝛥𝑇(.) For reference, the scale 0 to 1 represents a temperature difference of 11.4 +/- 1 °C, where the reported error is the standard deviation between daily values of 𝛥𝑇(. With these normalized temperatures, we can see what the performance might be like in a similar climate during a hot period (𝑇-. > 30.9 °C), relative to the prevailing mean and the current ‘gold-standard’ (thermal mass and night ventilation). While the consistent sub-ambient temperatures are promising, their variability day and night could cause discomfort (Figure 4A). One way to improve the indoor temperature stability is to add more thermal mass to the roof, which we explored theoretically after calibrating our model (Eq. 1 to 7) to the experimental data. We achieved this calibration by finding the heat transfer rates on the surface of the internal thermal mass that minimized the error between 𝑊$ measured and predicted from Eq. 5 (Figure 5E). We defined that error as the root mean square error Fortin et al. (2023) Cool running 10 𝑅𝑆𝑀𝐸=3∑(𝑃.2(*,3−𝑃-;2<,3)=>3?6𝑇 ( 13 ) where 𝑇 is the duration of the experiment, and 𝑃.2(*,3 and 𝑃-;2<,3 are the measurements and predictions at time 𝑡 during the experiment. We repeated the same process for 𝑊% on the radiator soffit, but with two convection rates, one for the period during the day when 𝑇%>𝑇(, and one for the night when 𝑇(>𝑇%, to account for the different modes of surface convection (Figure 5F). For 𝑊*+, on the sky-facing surface of the radiator, we found the effective heat transfer rate for 𝑃9:**=ℎ (𝑇(−𝑇%) that would minimize the error between 𝑊*+, measured and predicted from Eq. 9 with on-site measurements of 𝑃*8" and 𝑃"23,44 (Figure 5F). In this case, calibrating 𝑃9:** for two heat transfer coefficients, to capture two convection regimes day and night, did not improve the fit between the predictions and the measurements, since 𝑇% remained sub-ambient throughout the experiment. Furthermore, for simplicity, we assumed 𝑃9:** to be a function of 𝑇( (instead of 𝑇@A). In Figure 4B, we used our calibrated model to predict the temperature inside the test box assuming the roof radiator was twenty times thicker and therefore had twenty times more thermal mass (𝜌𝐶𝑝% 𝑉%). In this scenario, the aluminum sheet would increase from 6 to 120 mm. This extra mass stabilizes the roof temperature around a daily mean which, in turn, stabilizes the convective heat exchanges with the interior (WR). For reference, a concrete roof that was 129 (+/- 22) mm thick, where the uncertainty depends on the thermal properties, would have the same volumetric heat capacity per unit area (35). As shown in Figure 4C, the amount of thermal mass in the roof can be tuned for different objectives. The mean interior temperature does not significantly vary after a six-fold mass increase, and there are diminishing returns with interior temperature stability after a twenty-fold mass increase. These results help evaluate the cooling potential of additional roof thermal mass alongside broader architectural considerations, such as the roof’s structural performance and its embodied carbon footprint. In Figure 4E, we compare the distribution of the normalized temperature for the test radiator (light green) and the hypothetical radiator with more mass (green). The latter is stable enough to remain within the range of adaptive comfort while also staying below the prevailing mean ambient temperature. As such, Figure 4E suggests that stable, sub-ambient cooling is possible below the prevailing mean. In dry climates, this can be useful for maintaining comfort in hot periods (𝑇-. < 32°C) according to international standards for adaptive thermal comfort in naturally ventilated buildings (32). Note that the prevailing mean (𝑇-.) is not the same as the peak exterior temperature on any given day. Therefore, this approach could still work as peak exterior temperatures approach 37°C, so long as the night temperatures are sufficiently cool. In cases where the prevailing mean or peak exterior temperatures are too high to stay within the adaptive comfort threshold, this approach could still produce interior temperatures that are cooler and, therefore, safer during dangerous heat waves. In these extreme cases, ventilation rates could be reduced to maintain cooler temperatures. Seasonal adaptation Finally, in Figure 4F we consider the influence of the relative cooling 𝑊B/𝑊' on the daily mean temperature and ventilation flow rate inside both boxes, following the scaling by Chenvidyakarn & Woods (28, 36, 37). The temperatures are normalized with 𝜙=(𝑇!"−𝑇()/𝛥𝑇C and the flow rates with 𝑄∗=𝑄/𝑄C where 𝛥𝑇C and 𝑄C are the reference temperature excess and flow rate that would occur in steady state without any cooling. The reference flow rate 𝑄C is calculated from 𝛥𝑇C using Eq. 2, and 𝛥𝑇C is found by solving for the balance 𝑊'=𝑊#+𝑊& where 𝑊' is the constant 1.2 Watts heat input, 𝑊# is the ventilation heat exchanges defined in Eq. 3 and 𝑊&= 𝑈𝐴 ∆𝑇 is the Fortin et al. (2023) Cool running 11 steady-state envelope heat exchange. We calculated the two