A parabolic and hyperbolic numerical formulation of the boundary inverse heat conduction problems is considered in this paper. The control volume algorithm is combined with a digital filter method to estimate temperature and heat flux values on a surface of a body based on the temperature measurement inside the body. Numerical experiments were carried out to obtain the best value of the non negative coefficient of the hyperbolic equation using noisy and smoothed input data. The accuracy of the method is verified by comparison with a direct (analytical) solution of the problem. The influence of the relatively high noise into measurement data is studied.