In this paper we discuss certain cases of thermal instability in axisymmetric contact problems with heat generation and heat exchange. Two solids of revolution pressed against each other are considered. One of the solids rotates about its symmetry axis. A characteristic feature of the problem is that the distance between the centers of gravity of the solids cannot be greater than a certain value Published in Prikladnaya Mekhanika, Vol. 43, No. 1, pp. 134–144, January 2007.