Temperature is a function of pressure, volume, and the amount of the gas.
Once the gas is compressed and stable in a sealed container, it is low temperature. Liquefied gases are cold. However when you’re filling the tank – say, a scuba tank – then it does get warm in that process because as you identified, the gas is being compressed. that’s where the active process is
This is also why we should immerse these in a tub of water while they’re being filled, to safely dissipate the heat and also protect the tank.
But it is also why you must not expose containers of compressed gases to heat because they will .. rapidly decompress. (Boom)
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