In a fractured rock mass, the existence of discontinuities may generate preferential paths where the hydraulic flow velocities are frequently much higher than in the porous medium and heat advection tends to dominate over heat diffusion. In these cases, the standard Galerkin FEM method leads to oscillatory results and requires the use of stabilization methods. Thus, the current paper introduces a 3-D formulation to solve the large advection problem for zero-thickness interface elements –which may be used to discretize fractures in a FEM context–, based on a pre-existent Characteristic method. A verification example is presented, showing that the formulation exhibits a good performance to represent the heat transport by the fluid along zero-thickness interface elements.