A novel, simple iterative algorithm is used to calculate the temperature distribution in a finite medium for the case of non-Fourier (hyperbolic) heat conduction. In this algorithm the temperature is calculated explicitly in one simple calculation that is repeated for each time step as the heat wave propagates through the medium with constant speed. When the wave reaches a boundary of the medium, it bounces back and moves in the opposite direction. All simple initial and boundary conditions can be modelled. An example of using the algorithm for the case of a finite, thermally insulated medium is given, and the results are compared with an exact analytical solution.