Abstract: When the thermal properties of a material, i.e., the heat conduction coefficient and the heat capacity are temperature dependent, the heat conduction in the material is of nonlinear form and the corresponding Inverse Heat Conduction Problem (IHCP) is called nonlinear IHCP. In this paper, two estimation methods, Sequential Function specification Method(SFM) and Conjugate Gradient Method(CGM), are developed for the estimation of the time-variable surface heat flux from temperature measurements. The basic idea and detailed algorithm of these two methods are presented and both methods are applied to a typical exemplified case. It can be seen from the result that, although there are some differences of algorithm framework and computational efficiency between the SFM and CGM, both estimation methods are feasible and not sensitive to the measurement noise.