Bruno A. Boley was among the first to analyze thermally induced vibrations of beams and plates, a subject of paramount importance in various fields of engineering and space technology. The present paper is concerned with moderately thick plates within the Mindlin theory. A correspondence of the solution to the simpler one of an auxiliary prestressed thin plate with effective parameters is derived. By another projection the solution of the thermal deflection can be further reduced to that of two effectively stressed membranes. The correspondence of deflections is extended to moments and shear forces in the case of neglected rotatory inertia. The class of solutions, however, is restricted to simply supported plates with straight edge elements. The representation in the frequency domain is understood and frequency response functions for the deflection of parallogram plates are presented, where a Boundary Element Technique with Green's functions of rectangular domains is used.