Scubadoo,
The temp of a tank increases when filled from a compressor and somewhat less so if filled at equal rate from a bank. Once the tank cools it may experience a pressure drop varying between 200-300 psi depending on rate of fill. Originally, the tank heated up because heat produced in the air by compression is transferred to the tank walls. This will continue as long as the differential temperatures exist between the two. The differential is fed provided that more energy is released by compression and the tank cools to the environment. At this point, the metal by virtue of its weight holds a lot more heat than the air. Anything which can cause the metal to shed heat will drop the temperature of the air inside and cause the pressure to drop. Water baths are a common method. Metal to water causes heat to leave very rapidly due to physics of heat transfer. As was mentioned, the capacity potential of a big chunk of metal is considerable. The heat which is left in the relatively small mass of air will be sucked into the metal although at a slightly slower rate. If the tank is removed from the bath very quickly, this continuing heat transfer can be felt as a slight warming of the metal which continues for a minute or two. A slight warming of the metal translates to a big drop in air temp due to the different capacities. IOW, a big drop of the air temp at this point will only cause a slight warming of the metal because the residual amount of heat in the air is very little despite the higher temp. A bath is considered beneficial for purposes of one stop filling. If the bath has enough water and if some flow is ducted into the bath, the tank can be filled from the compressor without the necessity of overfilling to compensate for pressure drop. Alternately, the tank does not have to be topped off after a lengthy cool down period.
The relationship between heat and temp is not clear to everyone. One way to visualize this is to consider the Tokamak fusion core. It can create temps hotter than the sun but not enough heat to boil a glass of water. As Craig mentioned, it's all about molecular speeds.