The relevance of the discussed issue is caused by the necessity to reduce the weight and dimensions of high radiation heat exchange systems while improving their energy efficiency. This can be achieved by appropriate profiling ribbed elements. Such surfaces are widely used in various fields of modern technology. Therefore, the problems of radiative heat transfer of the developed surfaces are of special scientific and technical interest. The main aim of the study is to obtain a rather simple analytical method from mathematical point of view for calculating the temperature distribution in the ribs of variable cross section in the radiative heat removal from the surface. The methods: use of the proposed linearizing transformation that allows reducing the influence of the nonlinear term in the original differential equation of energy transfer. The results. The authors have proposed the approximate mathematical method based on obtaining lower and upper bounds of the temperature field. This method has an engineering perspective, it is reasonably accurate and at the same time, it is rather simple. In this case, the first two approximations are enough. The calculations given in the article, for trapezoidal ribs may also be used in the particular case for wedge ribs. The found mathematical limits for estimating the upper and lower values of the temperature field allow estimating the coefficient of thermal efficiency for the ribbed surfaces at radial heat exchange.