Abstract An inverse heat transfer problem is discussed to estimate simultaneously the unknown position and timewise varying strength of a heat source by utilizing differential evolution approach. A two dimensional enclosure with isothermal and black boundaries containing non-scattering, absorbing and emitting gray medium is considered. Both radiation and conduction heat transfer are included. No prior information is used for the functional form of timewise varying strength of heat source. The finite volume method is used to solve the radiative transfer equation and the energy equation. In this work, instead of measured data, some temperature data required in the solution of the inverse problem are taken from the solution of the direct problem. The effect of measurement errors on the accuracy of estimation is examined by introducing errors in the temperature data of the direct problem. The prediction of source strength and its position by the differential evolution (DE) algorithm is found to be quite reasonable.