Free convection heat transfer inverse problems are considered in order to recover the boundary condition unknown parameters. The process of inverse problem solution is based on the flow parameters measurements in a set of points inside a volume. The direct problem of free convection process is simulated by the time-dependent 3D Navier-Stokes equations (NSE). The system of NSE is solved by implicit finite difference scheme having second order accuracy for time and space variables. The numerical experiments confirm the feasibility to recover some parameters of internal heat source.