The research presented in this article is a contribution to the characterization of thermal dual analysis. The aim of a dual analysis based on two complementary numerical methods is to calculate the stationary temperature field. The two methods are respectively the classical Kinetically Admissible (KA) finite element or temperature method, and the Statically Admissible (SA) flow method. The originality of this work is twofold. First, it uses a flow approach (SA) in 2D and 3D that naturally respects flow conservation (in contrast to the KA method). Second, calculating the dissipation energy allows the exact solution of a problem to be enclosed, with the lower and upper bounds being calculated respectively by the KA and SA methods. Thermal bridges are areas of risk in the building walls, because they can give rise to uncontrolled increments in heat transfer. A number of studies have looked at thermal bridges, but much of the numerical code for building energy simulations uses heat transfer models based on one-dimensional heat flow analysis. Fabrizio Ascione (2014) showed that this can lead to unreliable results. The originality of this paper is to consider 2D and 3D thermal bridges using dual analysis with mesh sizes smaller than those used in conventional finite element approaches.