Dissipative losses of mechanical energy and the rate of heating of the scanning microscope probe in dynamic contact with the sample surface have been theoretically estimated for a small temperature difference between the probe and the sample. Time variation of the temperature and the power of nanoprobe heating (cooling) caused by the near-zone fluctuational electromagnetic field have been calculated. Averaged over the period of nanoprobe oscillations, this thermal power significantly exceeds the power of mechanical losses even for small local variations of the sample surface temperature. For this reason, heating of the probe can stimulate its additional damping. This may account for the discrepancy between theoretical and experimental values of dissipative forces.