We implemented loose and tight coupling methods to understand thermal diffusion between ocean and ice by means of a simplified one-dimensional model set-up proposed by Stefan. A Stefan problem is a prototypical two-phase model that can used to model, for example, melting and freezing of water due to the transfer of heat fluxes between the two phases. We discretized heat fluxes using low order derivatives for loose coupling and higher order derivatives for tight coupling while fluxes are computed at the (moving) interface. Compared to a known reference solution the tight coupling method exhibits a lower error when compared to the loose coupling discretization. However, further numerical tests are required to analyze these coupling methods.