This research aims to explore the relationship between the temperatures of solar corona and planetary magnetosheaths. Based on the second law of thermodynamics, the maximum temperatures of the planetary magnetosheaths cannot be higher than that of the solar corona. A theoretical investigation has been made on the expansion of solar corona, the propagation of solar wind and the compressions of planetary magnetosheaths by the bow shocks. The method used is general and fit for the dynamics of multiple components, thermal anisotropy, and non-Maxwellian plasmas in a steady state, and approximate formulas have been obtained. It is found that, for the steady situations, the temperatures of all the planetary magnetosheaths at the subsolar points in the solar system have comparable values, which are also close to the maximum temperature of the solar corona. Secondly, a systematic statistical survey on the average temperatures of the planetary magnetosheaths have been carried out, which show that, the average plasma temperatures of the magnetosheaths of Earth and Saturn are 183eV (2.12MK) and 172eV (2.00MK), respectively. The statistical results are consistant with the theoretical results. These results are very practical for the estimations of the thermal properties of the planetary magnetospheres.