The StarDICE experiment strives to establish an instrumental metrology chain with a targeted accuracy of 1 mmag in griz bandpasses to meet the calibration requirements of next-generation cosmological surveys. Atmospheric transmission stands out as a significant source of systematic uncertainty. Specifically, gray extinction induces spurious variations of photometric fluxes. We propose a solution relying on an uncooled long-wave infrared thermal camera to evaluate it. This type of camera can provide real-time insights into atmospheric conditions and detect cirrus clouds. However, achieving accurate measurements with thermal imaging systems necessitates prior calibration due to the influence of temperature-induced effects, which compromise their spatial and temporal precision. Moreover, these systems cannot provide scene radiance values in physical units by default. This study introduces a new calibration process utilizing a tailored forward modeling approach. The method is applied to an uncooled FLIR Tau2 thermal camera. It incorporates sensor, housing, flat-field support, and ambient temperatures, along with raw digital response, as input data. Experimental measurements are conducted inside a climatic chamber, with the camera imaging a thermoregulated blackbody source. Results demonstrate the calibration effectiveness, achieving precise radiance measurements with a temporal pixel root-mean-square error (RMSE) of 0.09 W/m2/srand residual spatial noise of 0.03 W/m2/sr.