In order to find an approximate solution of the heat equation under time-dependent boundary conditions, a research has been conducted as shown in the following steps. Firstly, with the power function of time being the temperature boundary condition, combined with the heat balance and refined integral methods, the standard polynomial approximation solution to the temperature equation has been adopted so as to obtain the relationship between the power of the approximate solution and the power of the temperature boundary function, thus working out the approximate solution. Secondly, an approximate solution expression will be constructed based on the application of the principle of superposition of linear differential equation, with the complex time dependent boundary condition taken into consideration. The experimental results show that this simple method, characterized with a better calculation accuracy, proves to be very effective in simulating the heat transfer process.