Total sky irradiance onto the Earth's surface includes contributions from solar (or shortwave) radiation as well as thermal (longwave) radiation. Whereas shortwave downwelling is only present during daylight hours, thermal downwelling radiation is present throughout the day and night. Sky thermal irradiance on the Earth's surface has been described in other references as a function of surface ambient temperature and relative humidity. In this study, we show that with the introduction of low overcast clouds (altitude less than 2km and 100% cloud cover), thermal downwelling sky irradiance increases 34%. A comprehensive model was developed to compute the thermal downwelling sky irradiance as a function of temperature, relative humidity, cloud height, and percent cloud cover. Based on ground truth measurements collected in Reston, Virginia, we propose coefficients to model the total thermal downwelling irradiance including cloud effects with an operational error of 9.7%.