This paper studies the multi-domain coupled system of one dimensional Arctic temperature field and establishes identification model about the thermodynamic parameters of sea ice (heat storage capacity, density and conductivity) by the so-called output least-square estimate according to the temperature data acquired by a monitor buoy installed in the Arctic ocean. By the optimal control theory, the existence and dependability of weak solution and the identifiability of identification model have been given. Moreover, necessary optimality condition is proposed. Furthermore, the optimal algorithm for the identification model is constructed. By using the optimal thermodynamic parameters of Arctic sea ice, the numerical simulation is implemented, and the numerical results of temperature distribution of Arctic sea ice are demonstrated.