A boundary element model to deal with heat and solute diffusion involving a moving interface is presented. The problem requires the solution of two parabolic partial differential equations invariable domains separated by a moving interface, whose temperature and velocity, as well as the concentration jump across it, are not know a priori but have to be determined as part of the solution. Moreover, the temperature of the interface is concentration-dependent while its velocity depends on both temperature and concentration gradients. To validate the scheme a test problem, which has an explicit similarity solution (analytical), is considered. Numerical results show that the boundary element method is very accurate, especially in regard to the concentration jump across the interface.