The solution method of the end surface temperature of noncontact mechanical seals was researched for the case of the temperature of seal ring face is difficult to measure in the project.The finite element model of heat transfer was established,and the heat transfer of the seal ring was calculated to obtain the steady state temperature distribution.The finite element equation was modified,two methods,the polynomial fitting and Trefftz equation approximation were presented to predict the end face temperature based on the modified computed results,and the accuracy of the two methods were compared.By reducing the number of known temperature nodes,this means the reducing of the amount of thermocouple used in engineering,the residual node temperature was calculated by using the modified interpolation function in the finite element equation.The influence of the number of known temperature nodes on the calculation results was discussed,and the prediction errors of different parameters were compared after determining the optimal value.Results show that the results obtained from the two methods are all increased with the increase of the rotating speed,and decreased with the increase of the temperature of the sealing medium,but the predicted results of the Trefftz equation are better than that of the polynomial.The results obtained by using 4 interpolation nodes are in good agreement with the exact solutions.