An inverse thermal problem is considered to determine the unknown inlet temperature for two-phase laminar flow in a parallel plate duct where conductive, convective and radiative heat transfer is involved. The inlet temperature is estimated by measuring gas temperatures at downstream of the duct. The inverse problem is solved by minimizing the objective function with regularization methods, i.e., the conjugate gradient method (CGM) and the Tikhonov regularization method (TRM). The effects of the functional form of inlet temperature profile, the number of the measurement points and the measurement errors are investigated. The accuracy and efficiency of these two methods are compared and discussed. Both CGM and TRM estimates the inlet temperature well, even when the radiation is involved. However, the TRM usually takes a longer computational time than the conjugate gradient method due to non-linearity in determining the sensitivity coefficient.