This paper presents a novel numerical solution algorithm for the linear transient heat conduction equation using the 'Explicit Green's Approach' (ExGA). The method uses the Green's matrix that represents the domain of the problem to be solved in terms of the physical properties and geometrical characteristic. The Green's matrix is the problem discrete Green's function determined numerically by the Finite Element Method (FEM). The ExGA allows explicit time marching with time step larger than the one required by FEM, without losing precision. The ExGA numerical results are quite accurate when compared to analytical solutions and to numerical solutions obtained by the FEM. (C) 2008 Elsevier Ltd. All rights reserved.