## 2 Method
### Design of the Mathematical Model  
The mathematical model was based on analytical calorimetry. The heat transfer equation can be written as a sum of heat flows (expressed in \(W\) per kg body mass):  
\[S=M\pm R\pm C\pm K-E_{resp}-C_{resp}-E \tag{1}\]  
where \(S\) is the body's heat storage (at equilibrium, heat gain is balanced by heat loss and so \(S=0\); for a neonate in this condition, homeothermy is reached, and the body's internal temperature stabilizes at between 36.5 and 37.5 \({}^{\circ}\)C), M is the metabolic heat produced by non-shivering thermogenesis in brown adipose tissue, R is radiative heat loss/gain (corresponding to the infrared radiation transferred between the skin surface and the various surfaces in the environment), C is convective heat exchanged by air moving over the skin surface and the upper airways (\(C_{resp}\)), K is the transfer of thermal energy from  
Figure 1: The 1500 g anthropomorphic mannequin wearing a head cap and a diaper. The mannequin is an anatomically faithful model of a small-for-gestational-age neonate. The anatomic shapes are important because they modify the heat exchange coefficients and, thus, condition heat exchanges with the environment. the mother's body to the neonate via skin-skin contact, and E is the evaporative heat loss through the skin and the upper airways (E\({}_{\rm{resp}}\)). The electric heat power supplied to the mannequin balances the dry heat losses (R + C + K). In a clothed mannequin, R + C are reduced by a coefficient of heat exchange due to clothing (F\({}_{\rm{cl}}\)). The degree of inter-infant variability in energy metabolism (M) was based on [PERSON] et al. 's measured range [15] from 1.11 to 2.70 W/kg. It should be noted that the mean value measured by these investigators (1.59 W/kg) was similar to that calculated by [PERSON] et al. on the first day of life for a neonate weighing 1500 g [26]. Evaporative losses through the respiratory tract (E\({}_{\rm{resp}}\) W/kg) [27] were modeled as:  
\[\rm{E_{resp}}=0.0173\ M\ (\rm{P_{e}-P_{i}})\frac{A_{D}}{W_{t}} \tag{2}\]  
where \(\rm{A_{D}}\) is the total body surface area (m\({}^{2}\)), \(\rm{W_{t}}\) is the body mass (kg), and (\(\rm{P_{e}-P_{i}}\)) is the difference in water vapor pressure between exhaled and inspired air (kPa). The respiratory convective heat loss (C\({}_{\rm{resp}}\), W/kg) was modeled as the heat exchanged by air moving out of the respiratory tract [27]:  
\[\rm{C_{resp}}=0.0014\ M\ (\rm{T_{e}-T_{i}})\frac{A_{D}}{W_{t}} \tag{3}\]  
where (\(\rm{T_{e}-T_{i}}\)) is the difference between the expired air temperature (\(\rm{T_{e}}\)) and the inspired air temperature (\(\rm{T_{i}=T_{a}}\)) (\({}^{\circ}\)C) and M is the energy metabolism (\(\rm{W/m^{2}}\)). \(\rm{T_{e}}\) was calculated according to [PERSON]'s equation [28]:  
\[\rm{T_{e}}=32.6+0.066\ T_{a}+32\ M_{H_{2}O} \tag{4}\]  
where \(\rm{T_{a}}\) is the air temperature and \(\rm{M_{H_{2}O}}\) is the mass of air vapor in the inspired air (g/L). The water evaporation through the skin (E, \(\rm{W/kg}\)) was modeled as:  
\[\rm{E}=\rm{he}\ \omega\ Ae\left(P_{SH_{2}O}-P_{aH_{2}O}\right)F_{pd}\frac{A_{D}}{W_{t}} \tag{5}\]  
where he is the heat transfer coefficient by evaporation (\(\rm{W/mb/m^{2}}\)) calculated from the Lewis relation (\(\rm{h_{e}=1.67\ h_{c}}\)), \(\rm{\omega}\) is the fraction of body area that is wet (dimensionless; 0.06 when the skin is dry [29] and 1 when the skin is completely wet, as in an undried neonate), \(\rm{PS_{H_{2}O}-P_{H_{2}O}}\) is the water vapor partial pressure difference between the skin (the saturation pressure for mean skin temperature) and air (mb), Ae is the skin surface area that exchanges by evaporation (0.805, calculated by subtracting the manikin-mattress contact area (0.195) from the total body surface area, and \(\rm{F_{pd}}\) is the reduction in the coefficient of latent heat exchange due to clothing (dimensionless).