Many inverse heat transfer problems can be solved efficiently through the minimization of a performance function utilizing the conjugate gradient method. The gradient of the performance function needed in the minimization procedure of the conjugate gradient method is obtained by employing either the adjoint variable method or the direct differentiation method. In the present study we consider an inverse problem of estimating time-varying strength of a heat source in a two-dimensional heat conduction system, and compare the adjoint variable method and the direct differentiation method in terms of accuracy and computational efficiency, and finally suggest a new method that exploits the advantageous aspects of both methods while avoiding the shortcomings of them.