This paper compares several methods of finding the surface heat flux using transient temperature measurements inside a heat-conducting body. Experimental data is used with a known heat flux history. The methods include function specification with several future approximations, Tikhonov regularization, iterative regularization and specified functions over large time regions with Green’s functions. The first three methods are used with the residual principle and the results are quite similar. If the heat flux has a simple time variation over large time regions, taking advantage of that feature can improve the results, as shown by the Green’s Function analysis.