In this paper, the author presents a parallel implementation of the summation of slow-converge series that describe the three-dimensional heat distribution. Thermal field arising from electrical heating system situated into concrete floor, is computed by complicated three-dimensional series. The heater is approximated with two-dimensional Dirac's distribution (X, Y axes) and a gate function, which describes the positions of the cables on Z-axis. It is necessary to stress that the total computation time of the series, depends on the summation of the series of elements, which are close to discontinuity points (Dirac's distribution). The author uses an analytical solution, and implements a parallel algorithm that accelerates considerably the computation for the total space. The computations are done with the use of an MPI library on Hitachi SR 2201 parallel computer. The author stresses on the aspect of the efficiency of this research.