Inverse analysis utilizing the conjugate gradient method is used to estimate the timewise varying strength of a line heat source placed at a specified location in a rectangular region with insulated boundaries. No prior information was used on the functional form of the source strength with time. Transient temperature recordings taken at the boundaries of the region served as the simulated experimental data needed as input for the inverse analysis. In order to test the accuracy of the inverse analysis under most strict conditions, timewise variation of the source strength is chosen in the form of rectangular, triangular, and sinusoidal functions. Both the regular iterated and modified conjugate gradient method are used for solving the inverse problem. The modified conjugate gradient method often provided the answer with smaller number of iterations when the initial condition for the unknown function was available.