The internals of the valve are likely to be very close to the cooling water temperature during gas operation due to the low heat transfer coefficient on the gas side. The surface temperature of the check valve at the inlet and exit are not the same as the gas temperature inside the valve. I would suggest calculating an inside heat transfer coefficient based on gas flow through the check valve and an outside heat transfer coefficient for water through the jacket. Utilizing these two values together with the metal thickness and conductivity you can calculate the inside and outside wall temperatures of the jacketed valve.
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