A thin heat-conducting adhesive layer is considered in a two-dimensional approach. The material of the adhesive layer exhibits an arbitrary non-homogeneous thermal conductivity which is a function of the spatial coordinate perpendicular to the interface. Based on the weighted residual method, a new finite element formulation for a four-node, rectangular element is derived which is able to easily incorporate high conductivity gradients in the new thermal conductivity matrix. The approach is not based on any assumptions of the temperature distribution (e. g. linear or cubic) but considers that the heat flux must be constant in the case that no heat sources or sinks are present. A numerical example of a simple bonded joint illustrates the implementation into the commercial finite element code MSC. Marc due to special user subroutines. The numerical results are compared to a classical approach based on standard elements and the differences are discussed. (C) Koninklijke Brill NV, Leiden, 2008