The analysis of the dynamics of ice growth and melting over the sea water is presented by this paper. According to the system of equation proposed by Hibler 3 thermal regimes are possible: ice growth due to atmospheric cooling, ice melting due to oceanic warming and ice melting caused by the heat income from both atmosphere and ocean. All these regimes are analyzed by means of the ice thermodynamics model that is introduced in the paper. The parameterizing procedure for ocean mixed-layer is also suggested here. ID numerical modeling results indicates the ability of the model to reproduce basic ice thermodynamic processes adequately. All the results are considered as a preliminary ones on the way to build a complete 3D model of the ice dynamics over the Arctic Ocean.