## 3 Results
### Heat Losses  
We have plotted the heat loss function Equation (8) as a function of the skin temperature \(T_{skin}\) in several realistic conditions. The results are presented in Figure 1. On panel a: \(q(T_{skin})\) is plotted for various values of the ambient temperature \(T_{\infty}\) (22 \({}^{\circ}\)C--blue line, 25 \({}^{\circ}\)C--red line, 27 \({}^{\circ}\)C--green line). On panel b: \(q(T_{skin})\) is plotted for various values of the relative humidity, \(RH\) (40%--blue line, 70%--red line, 100%--green line), \(T_{\infty}\) = 30 \({}^{\circ}\)C. On panel c: \(q(T_{skin})\) is plotted for various values of the skin wetness, \(W\). (\(T_{\infty}\) = 22 \({}^{\circ}\)C, \(W\) = 0--blue line, \(T_{\infty}\) = 22 \({}^{\circ}\)C, \(W\) = 1--red line, \(T_{\infty}\) = 27 \({}^{\circ}\)C, \(W\) = 1--green line). Skin emissivity \(\varepsilon\) was set to 0.98. The obtained expression for the heat loss Equation (8) contains non-linear terms, which complicates the analytical analysis. Fortunately, looking into Figure 1, one can see that the combined heat loss is very close to a linear function of the temperature gradient \(T_{skin}-T_{\infty}\). Thus, for realistic conditions of the thermographic assessment in a controlled environment, we can linearize the heat loss function in a narrow range of parameters. As a result, we can get a linear approximation for heat loss that accounts for radiative, convection, and evaporative mechanisms  
\[q\ =\ q_{0}+h(T_{skin}-T_{\infty}) \tag{15}\]  
where \(h\) is an effective heat transfer coefficient. This expression can be substituted into boundary conditions Equations (11) and (14). \(q_{0}\) can be obtained explicitly from Equation (8) (\(T_{skin}\) = \(T_{\infty}\)), and \(h\) can be obtained from the linearization of Equation (8) at room temperature. \[ \begin{split} h\ =\ 4\varepsilon\sigma T^{3}+\frac{5h_{c}}{4}0.061 \big{(}9.66\times 10^{-4}+5.45\times 10^{-3}h_{c}W\big{)}P_{sat}(T_{\infty})e^{0.061(T-T_{\infty})}\\ +5.45\times 10^{-3}\frac{h_{c}P_{\mathrm{att}}(T_{\infty})W}{4(T-T_ {\infty})}\Big{(}e^{0.061(T-T_{\infty})}-RH\Big{)}\end{split}  \tag{16}\]  
Figure 1: The dependence of the heat loss function, \(q\) [W/m\({}^{2}\)], on the skin temperature \(T_{skin}\) [\({}^{\circ}\)C]. (**panel a**): \(q(T_{skin})\) for various values of the ambient temperature \(T_{\infty}\) (22 \({}^{\circ}\)C—blue line, 25 \({}^{\circ}\)C—red line, 27 \({}^{\circ}\)C—green line), (**panel b**): \(q(T_{skin})\) for various values of the relative humidity, \(RH\) (40%—blue line, 70%—red line, 100%—green line), \(T_{\infty}\) = 30 \({}^{\circ}\)C. (**panel c**): \(q(T_{skin})\) for various values of the skin wetness, \(W\). (\(T_{\infty}\) = 22 \({}^{\circ}\)C, \(W\) = 0—blue line, \(T_{\infty}\) = 22 \({}^{\circ}\)C, \(W\) = 1—red line, \(T_{\infty}\) = 27 \({}^{\circ}\)C, \(W\) = 1—green line). Skin emissivity \(\varepsilon\) was set to 0.98. \[q_{0}\ =\ \left(9.66\times 10^{-4}+5.45\times 10^{-3}h_{c}W\right)\ P_{sat}(T_{ \infty})(1-RH) \tag{17}\]  
which needs to be evaluated at \(T_{\infty}\). The last term of Equation (16) is specific for free convection flow. It diverges for \(RH<1\) and \(W>0\), which is manifested as the increased slope near \(T=T_{\infty}\) on Figure 1c. For practical purposes, Equation (16) can be evaluated at some small distance from \(T_{\infty}\) (e.g., 0.5 \({}^{\circ}\)C off, where the temperature dependence becomes linear). Alternatively, it can be evaluated numerically. The effective heat transfer coefficient, \(h\), at room temperature can be estimated as 12 W/m\({}^{2}\)/K for dry skin (\(W=0\)) and 21 W/m\({}^{2}\)/K for wet skin (\(W=1\)).Therefore, we will use \(h=12\) W/m\({}^{2}\)/K for dry skin as a baseline in the further calculations.