The aim of the present paper is to propose a general methodology for the numerical modelling of both anti and de-icing systems. A lubrication model is used for dealing with the dynamics of the runback water film. As regards thermal effects, in order to take into account heat conduction and unsteadiness, a parabolic temperature profile is assumed with respect to the normal coordinate for the ice layer. Heat transfers in the airfoil solid structure are described using a dedicated solver based on the unsteady heat conduction equation. The most original contribution of this work is the new technique (herein referred to as the "improved Schwarz method") which is proposed for coupling in a robust way the accretion-runback model and the solid heat conduction model. This new coupling algorithm allows to ensure fast convergence of both temperature and heat flux at the coupling interface (airfoil outer surface) and can be used either for steady state computations (anti-icing mode) or unsteady computations (de-icing mode). Numerical test cases which have been performed so far are very promising and show the relevance of this new approach for real applications and 3D extension.