Under strong laser radiation action on solids and liquids, all the thermophysical parameters which characterize these media become dependent on the medium temperature. Assuming for the coefficients \lambda(T) and c\rho(T) to be linearly changed by the temperature, the non-linear inverse problem of heat conductivity is resolved. The problem is resolved for two cases: 1) For solids and fixed liquids and 2) For heat conductivity with liquid laminar convection due to laser radiation action. The parameter \gamma, describing the gradient of coefficient of the heat conductivity, is calculated and the influence of liquid convection on \gamma is estimated. It is considered how the Bi number affects the final result. A developed algorithm for solving inverse problem may be used for finding the exact analytical solution of some problems of diffusion and fluid mechanics.