Monte Carlo calculations have been made of the rarefaction of the filling gas in a magnetron sputtering discharge due to collisional energy transfer from the flux of sputtered atoms. Temperature profiles of the filling gas between parallel cathode and substrate planes were calculated for both Ar and Ne filling gases and for C, Al, Ti, Cu, W and Au sputtered atoms. The effects of filling gas pressure, discharge voltage and current and cathode-substrate separation were also studied. At constant filling gas pressure, and in the limit of high discharge current, the maximum temperature was approximately proportional to the square soot of the discharge current; for constant pressure and discharge voltage and current, the maximum temperature increased linearly with the cathode-substrate separation. The heating of the filling gas was greater for Ar than for Ne, due to differences in the thermal conductivity, sputtering yield, collision cross section, and average fraction of energy transferred from sputtered atoms in a collision. The magnitude of heating also depended strongly on the material being sputtered, primarily being determined by the sputtering yield, particularly at high pressures, and to a lesser extent by the collision cross section, masses, and binding energy of the sputtered and filling gas atom combination. Negligible heating of Ar was calculated for C as the sputtered material, while maximum rarefaction was produced using Au for the same discharge conditions.