To commute between the different resistance states of a magnetic tunnel junction (TJ) one can use a thermally-induced pinned layer switching mechanism. When a sufficiently high electrical current flows through the insulating barrier, local temperatures inside the tunnel junction can increase above the blocking temperature of the antiferromagnetic layer used to pin the magnetization of the adjacent ferromagnet. Then, it is possible to switch the magnetization of the pinned layer with a small magnetic field H and thus revert the magnetic state of the TJ. Here we demonstrate thermally-induced pinned layer switching in thin magnetic tunnel junctions. We further present numerical results that suggest that heating is small when one takes into consideration the uniform current density flowing through the tunnel junction and that one must conclude that nanoconstrictions concentrate most of the current, increasing local current densities and temperature. Simulation of heating and cooling times demonstrates that current-induced pinned layer switching is a competitive mechanism for actual technological applications.