  We study analytically and numerically a problem of self-heating in small mesa
structures. Our results show that the self-heating is proportional to a
characteristic in-plane size of the mesa. Experimental data for small
high-$T_c$ superconductor Bi2212 mesas are in qualitative agreement with our
calculations. We estimate the self-heating in Bi2212 mesas with different sizes
and demonstrate that the self-heating can effectively be obviated in small mesa
structures.
