In this paper, a new and simple boundary-domain integral equation is presented for heat conduction problems with heat generation and non-homogeneous thermal conductivity. Since a normalized temperature is introduced to formulate the integral equation, temperature gradients are not involved in the domain integrals. The Green’s function for the Laplace equation is used and, therefore, the derived integral equation has a unified form for different heat generations and thermal conductivities. The arising domain integrals are converted into equivalent boundary integrals using the radial integration method (RIM) by expressing the normalized temperature using a series of basis functions and polynomials in global co-ordinates. Numerical examples are given to demonstrate the robustness of the presented method.