The environmental boundary conditions of the building exterior surface could be expressed in terms of the sol-air temperature T o and the heat transfer coefficient h o. This has previously been derived by applying Thevenin's theorem to the linear thermal network model of the convective and radiative environment. Here, the sol-air thermometer, previously used only for measurement of T o , was applied for accurate measurement of h o. The step-transient method was used, where the temperature of the sol-air thermometer was initially raised to above T o and then monitored during its transient return to thermal equilibrium. This method was validated by (1) comparison of h o results against values obtained with a steady-state method and (2) comparison of predicted heat flux against the electrical heater power, supplied for validation purpose. Accurate results were obtained, with 7.3% measurement uncertainty. The present solair thermometer time constant t was around 1 h. Based on predictions from dynamic modelling, the t could be reduced 10-fold, with only small effects on the accuracy from heat loss through the insulation layer.