Auger electron spectroscopy and thermoresistive methods are used to study the physical processes leading to gas cooling of heated molybdenum filaments in a wide temperature range of 350-1300 K and pressures of 760-10-3 Torr, corresponding to the operating range of a Pirani-type vacuum sensor. Nitrogen was used as the gas. It is shown that nitrogen atoms chemisorbed on the surface do not contribute to gas cooling, which occurs only due to physisorbed N2 molecules. In the intermediate vacuum region of 10-3-1 Torr, the heater is cooled due to the equilibrium between the flux of incident and thermally desorbed molecules, which is well described by the Hertz--Knudsen formula and first-order desorption with an activation energy of ~0.55 eV. On the contrary, at high pressures close to atmospheric, this cooling occurs due to the thermal desorption of gas molecules from an almost filled monolayer, which reduces its relative efficiency by many orders of magnitude. Keywords: vacuum, adsorption, Pirani sensor, molybdenum, thermal desorption, nitrogen.