It is demonstrated that the thermomagnetic stability of composite superconductors can be considerably increased by introducing into them a small quantity of a material with an extremely high specific heat at low temperatures. Measurements show that the criterion of “adiabatic” stability for a (Nb3Sn + 7 vol. % PrB6) wire is 70% higher than for a reference Nb3Sn wire (at 4.2 K, the specific heat of the doped sample is seven times higher than that of the reference sample). For a (NbTi + 5vol. % Gd2O2S) sample, the specific heat of which at 4.2 K is nine times higher than that of a reference NbTi wire, this increase in stability is as small as 10% (because the characteristic thermal time in the transverse direction is much longer than the time of the magnetic flux jump development).