At present, there exists a trend for spacefaring countries to use methane as fuel for the first stages of launch vehicles. Russia is currently developing a promising launch vehicle known as Amur LNG. However, due to methane being a hazardous (flammable and explosive) substance, it is poorly suited for fuel tank strength tests conducted using existing equipment. In this regard, we face an urgent issue of developing a safe method for simulating liquid methane temperature during strength testing of methane tanks. We propose to cool the tank with a nitrogen vapour-liquid mixture. To estimate cooling time for a cryogenic tank treated with a nitrogen vapour-liquid mixture as per the method proposed, along with determining the amount of refrigerant to be used, we solved its thermal state problem using the method of isothermal nodes. This approach may also be used for oxygen tanks.