The physical-mathematical model and a numerical method for solving the nonstationary two-dimensional one-fluid (one-temperature) Reynolds equations closed with turbulence models, taking into account the diffusion and thermal conductivity processes for bodies of simple geometric forms were described and verified. The effects of the temperature field inside the streamlined body and at changing its shape under the action of temperature stresses were analysed. Temperature fields and thermal stresses in the simple structural elements have been obtained. The corrections to the value of convective heat flux due to non-uniform surface temperatures, the presence of temperature gradients and the shape change may be significant and have to be considered to increase the accuracy of aerothermodynamic modelling.