A method is developed for estimating the nonradiative heating of stellar chromospheres by measuring the net radiative losses in strong Fraunhofer line cores. This method is applied to observations of the Mg II resonance lines in a sample of 32 stars including the sun. At most a small dependence of chromospheric nonradiative heating on stellar surface gravity is found, which is contrary to the large effect predicted by recent calculations based on acoustic-heating theories.