It is supposed that with the climate variability, the temperature of the ocean surface begins its raising by 0.03 degree annually during 50 years and then decrease up to primal value for 50 years. The climatic model of the ocean with 24 levels on a vertical is further integrated for the period of 1200 years and simulates penetrations of warming from the surface deep into the ocean. A three-dimensional equation of transport of dissolved methane from sources is simultaneously solved, which are included in that moment, when warming reaches the area of methanehydrate stability and raises the temperature by a defined magnitude - tolerance of 0.1 degrees. Two experiments with different sources of methane were carried out. When the sources of methane are located on the shores of the Arctic and the Southern Oceans only, the flux of methane into the atmosphere after 50 years has reached 2.1 Tg and after 82 years it has become maximum 2.64 Tg. In the other experiment, the flux of methane into the atmosphere has exceeded 4.8 Tg after 50 years, and has reached maximum 12.7 Tg after 150 years.