In this paper we focus on the numerical simulation of the steady state heat conduction in a three dimensional enclosure geometry without the presence of heat source. This physical phenomena is governed by a boundary integral equation of the second kind. For the discretization of the boundary integral equation we have used the boundary element method based on the Galerkin weighted residuals method. The system of linear equation which subsequently arise has been solved by the conjugate gradient method. To demonstrate the high efficiency of this method a numerical experiment has been constructed.