Both the temperature and the carrier density dependence of the mobility of two-dimensional electron gases in a Si/SiGe heterostructure are studied based on the scattering theory. The calculated results show that the mobility due to remote ionized impurities increases with an increase in temperature, whereas that due to background impurities decreases. The calculated mobilities are compared with the temperature and the carrier density dependence of the measured mobility. It is found that the scattering by background impurities dominates other scattering mechanisms.