The problem of simplifications for solving problems of cooling / heating of bodies under the joint action of convection and radiation is considered. The mathematical formulation of the problem of non-stationary nonlinear heat, allowing along with convection, to take approximately into account the heat radiation. The solution of the problem for a thin body thermal model, based on the substitution method, linearizing the right boundary condition, as well as through the integral equation relationship between heat flow and surface-average and mass – average temperatures for the simple bodies in a regular stage of thermal conductivity. Two engineering methods were developed for calculating the temperature fields and axial thermal stresses during cooling (heating) bodies of simple shape in the form of a plate, ball, and cylinder by convection and radiation in quasi-stationary stage. It is shown that neglecting heat transfer by radiation can lead to significant errors in calculation of the temperatures (up to 26%). The adequacy of the solutions has been tested at extreme cases, in the lack of heat transfer by radiation.