The study provides the results of experimental tests on temperature distribution throughout the surface of a corrugated metal sheet. Mathematical models are proposed for calculating the thermal conductivity and the thermal stress state of a fragment of the corrugated metal frame of a transportation facility whose lateral surfaces are heated to different temperatures. It is assumed that the temperature depends on two spatial variables. As a possible criterion for choosing the desired function of temperature distribution throughout the construction, it is assumed that the functional defined by a set of admissible functions is minimized in the form of an integral throughout the region of the body from the expression given by the production of entropy. In the study of the temperature field, the differential equation of thermal conductivity is used, and the stress-strain state is measured by the equation of the theory of thermal elasticity. To solve the differential heat equation, the method of finite differences is used, and for the solution of the equations of the theory of thermal elasticity, the finite element method is applied. It has been established that the temperature is distributed unevenly throughout the corrugated metal sheet. There is a temperature difference between the lower and upper surfaces of the corrugated metal sheet. The temperature difference between the bottom and top sides of the sheet is +7.1 °C at the highest atmospheric temperatures and –5.5 °C at the lowest atmospheric temperatures. It has been determined that the magnitude of the stresses that appear on corrugated metal sheets due to the atmospheric temperature difference is up to 25 % of the permissible stress. Therefore, when designing corrugated metal structures, it is necessary to calculate the effect of climatic temperature changes. The obtained data of the thermal stress state of corrugated metal structures are important for design enterprises. It is because taking into account the action of the temperature field on the stress state of the structure as a whole at the design stage helps select materials to reduce the temperature stresses that have a direct influence on the development of corrosion damage to the metal of the pipe.