We formulate the problem of thermoelasticity for a bimaterial body with interface crack with regard for the contact of its faces in the central part under the action of thermal strains caused by a heat flow perpendicular to the interface. The components of the bimaterial have different heat-conduction coefficients and linear coefficients of thermal expansion. The crack is filled with a heat-conducting medium and its faces have thermal resistance caused by the presence of thin surface films. The problem is reduced to a system of nonlinear singular integrodifferential equations for the jump of temperature between the crack faces and the crack opening displacements. For the solution of this problem, we develop an iterative algorithm based on the method of successive approximations. We analyze the influence of heat flow and thermal resistance of the films on the size of the contact region of the crack faces, crack opening displacements, jump of temperature between the crack faces, and the stress intensity factors for interface stresses.