## Appendix A View Factors and Operative Temperature Formulas  
The view factors for a small area parallel or perpendicular to a surface of height \(a\) and width \(b\), separated by a distance \(c\), hold respectively as [25]  
\[F_{p-A_{i}}=\frac{1}{2\pi}\left(\frac{X}{\sqrt{1+X^{2}}}\arctan\frac{Y}{\sqrt{1+ X^{2}}}+(X\leftrightarrow Y)\right), \tag{10}\]  
with \(X=a/c,Y=b/c\), and  
\[F_{p-A_{i}}=\frac{1}{2\pi}\left(\arctan\frac{1}{Y}-\frac{Y}{\sqrt{X^{2}+Y^{2} }}\arctan\frac{1}{\sqrt{X^{2}+Y^{2}}}\right), \tag{11}\]  
with \(X=a/b,Y=c/b\). We should remark that the calculation of mean radiant temperatures for the perpendicular surfaces is extremely sensitive to how the above view factors are implemented. For example, in Section 3.1 we discussed panel radiators of varying height \(h\) that are installed on the cold wall, at 15 cm from the floor. In this case, one could naively compute the view factor from the lower edge of the cold wall up to the top of the radiator (\(a=h+15\) cm), or alternatively ignoring the 15 cm displacement (\(a=h\)). It can be shown that the view factor differs critically for both cases and returns a non physical result for the operative temperature. The reason is that the above functions are not linear in \(a,b,c\): since the view factors are additive, a more correct way to calculate them with Formulas (10) and (11) consists of subtracting \(F_{p-A_{i}}\) at \(a=h\) from \(F_{p-A_{i}}\) at \(a=h+15\) cm. This way one obtains a _net_ view factor, which despite not being 100% accurate, returns physical operative temperatures that match earlier results [24; 36] and the present numerical simulations (see e.g., Figures 20 and 21). We conclude with a few considerations about the definition of operative temperature adopted in this paper. In Section 2 we remarked that IDA ICE uses the simple arithmetic average of air temperature \(t_{air}\) and mean radiant temperature \(\bar{t}_{r}\), Equation (3). On the other hand, for the analytical calculation we used the exact formula for computing the op.t., Equation (4). The \(A\) coefficient is expanded as  
\[A\equiv\left(1+\frac{h_{r}}{h_{c}}\right)^{-1}, \tag{12}\]  
and we express \(h_{c}\) and \(h_{r}\) in function of the air and mean radiant temperatures by means of the following [37; 38; 39]: the heat transfer coefficient for radiation is written as  
\[h_{r}=\sigma\epsilon_{cl}\frac{A_{r}}{A_{D}}\frac{(t_{cl}+273.15)^{4}-(\bar{t }_{r}+273.15)^{4}}{t_{cl}-\bar{t}_{r}}\, \tag{13}\]  
where \(\epsilon_{cl}\) is the emissivity of a clothed person and \(A_{r}/A_{D}\) the ratio of the body radiation area (0.67 for crouching, 0.7 for sitting and 0.73 for standing). \(\epsilon_{cl}\) lies typically in the range 0.8-0.9 [40], here we use \(\epsilon_{cl}=0.9\). It can be shown that a 0.1 difference in the emissivity is marginal to the operative temperature, inducing an \(\mathcal{O}(0.001)\) difference in \(t_{op}\), which is less than 0.1%. The same holds for the ratio \(A_{r}/A_{D}\), as it is evident from Equation (13); in this paper we choose \(A_{r}/A_{D}=0.7\). \(\sigma=5.67\times 10^{-8}\) W/(K\({}^{4}\)m\({}^{2}\)) is the Stefan-Boltzmann constant. The convection coefficient holds instead as  
\[h_{c}=2.38\sqrt[4]{t_{cl}-t_{air}}\, \tag{14}\]  
if \(2.38\sqrt[4]{t_{cl}-t_{air}}>12.1\sqrt{V_{air}}\), otherwise  
\[h_{c}=12.1\sqrt{V_{air}}\, \tag{15}\]with \(V_{air}\) [m/s] the air velocity relative to the human body. Since for our room the air ventilation rate is 1 ACH, \(V_{air}\) is very small, of \(\mathcal{O}(0.01)\) m/s, therefore we use Equation (A5). The clothing surface temperature for a sitting person doing office work can vary depending on the clothing; moreover, the exact calculation is rather involved and based on a recursive formula [39]. Considering three cases \(t_{cl}=23,\ 25,\ 31\ ^{\circ}\)C, which are shown in Figure A1, one can see a small impact of \(t_{cl}\) on \(t_{op}\). In particular, \(t_{cl}=25\ ^{\circ}\)C reproduces the IDA ICE values almost exactly.