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To provide efficient investigations for engineering problems related to heating/cooling process in solids, the effect of thermosensitivity (the material characteristics depend on the temperature) should be taken into consideration when solving the heat conductivity problems (Carslaw & Jaeger, 1959; Noda, 1986; Nowinski, 1962; Podstrihach & Kolyano, 1972). It is important to construct the solutions to the aforementioned heat conduction problems in analytical form. This requirement is motivated, for instance, by the need to solve the thermoelasticity problems for thermosensitive bodies, for which the determined temperature is a kind of input data, and thus, is desired in analytical form. In general, the model of a thermosensitive body leads to a nonlinear heat conductivity problem. It is mentioned in (Carslaw & Jaeger, 1959) that the exact solutions of such problems can be determined when the temperature or heat flux is given on the surface by assuming the material to be “simply nonlinear” (thermal conductivity t  and volumetric volumetric heat capacity v c depend on the temperature, but the relation, called thermal

Heat Conduction Problems of Thermosensitive Solids under Complex Heat Exchange