The KRC numerical thermal model has been used in the analysis of observations from virtually all Mars missions with infrared sensors and for the selection of virtually all Mars' landing sites. It uses a physics-based one-layer atmosphere gray at solar and thermal wavelengths to determine the radiative effect of a dusty atmosphere. One gas component may condense to form a seasonal polar cap and affect the global surface pressure. The atmosphere may be omitted entirely to model airless bodies. KRC uses layers that become thicker geometrically with depth and it uses repeated time step doubling. The surface may be homogeneous or have two zones of material properties, each zone may have temperature-dependent thermal conductivity and specific heat. Surface slopes or depressions are modeled to first order. Here KRC is described in detail and used to compute globally the annual average surface temperature accounting for albedo, thermal inertia, elevation, slope at 3 km resolution, and zonal climate. Comparisons with three other thermal models are discussed. The model is available for general use.