The present paper deals with a nonlinear unsteady heat flux calculation in the case when measurements are provided by only one thermocouple (TC) embedded in the material and the spatial shape of the unknown surface heat flux is given. This inverse problem is solved with the Conjugate Gradient Method (CGM) combined with the adjoint state, the direct problem being solved with the finite element method. This heat flux estimation technique is illustrated in the case of the plasma facing components located in the JET tokamak divertor that can be exposed to several MW.m­2 during more than 10 seconds. In those tiles, few embedded thermocouples (TC) located 1cm below the tile surface are used to measure the bulk temperatures of the Carbon Fiber Composite (CFC) composite tiles (which are coated with 14µgm of tungsten for the International Thermonuclear Experimental Reactor (ITER) like wall). A numerical study is first presented in order to validate the heat flux calculation and to study the accuracy of the method. Then experimental data from a recent shot with the ITER-like wall configuration are used in the heat flux calculation presented here. Results are compared with those obtained with the deconvolution technique in the linear case, on a simplified geometry of the tiles.