In this article a method of an approximate solution of a parabolic initial boundary value problem is presented. As an example the heat conduction equation is considered. This method consists of introducing some fictitious heat sources outside the region under consideration and choosing some points at the boundary of the region where the boundary conditions are strictly satisfied. The intensities of the sources are assumed to vary stepwise in time. The method may also be applied to the solution of inverse problems of heat conduction. Numerical results are given for some illustrative problems.