A heat and mass transfer problem of geophysical interest involving coexisting phases is studied. The dynamical system considered is the atmosphere-hydrosphere-cryosphere, wherein the spatial degrees of freedom along the vertical and longitudinal directions have been lumped. The reduced one-dimensional system is modelled by a simple, yearly averaged, energy balance model taking into account the coupling between the two phases present: the ice sheets and the ocean. This is done self-consistently by introducing a Stefan type of boundary condition at the interface. The resulting balance equation is linearized and solved analytically using mode truncation and Galerkin's method. The analysis is centered on the stability of the present-day climatic regime with respect to small excursions of the ice boundary. Special emphasis is put on the thermodynamic aspects, as well as on the characteristic time scales of evolution.