HPM can apply to not only the analysis of the solid mechanics but also the problem of the scalar field. For example, in the case of heat transfer analysis, a weak continuity of the temperature can be satisfied between subregion by using a penalty function. If this method is used, in the case of steady state problem, a solution of the accuracy that is equivalent to analytical solution is computed. However, like the case of the dynamic problem in the solid mechanics, the influence of the penalty function to the solution is not enough discussed in time integration in the unsteady problem. In this paper, it applied the Crank Nicholson method which is the implicit method to time integration, and verified accuracy of solution. As a result, even if it used the penalty function, the accuracy comparable as analytical solution was obtained.