Unless you overfill your tank, there is no way to get a quick, fill-while-you-wait full fill. Unless perhaps someone has a cryogenic fill station.
Leave your tanks overnight. From my discussions with multiple LDSs, the general consensus seems to be it takes a good 6 hours for the heated gas to cool in a freshly-filled cylinder. If they top it off in the morning (or perhaps that evening, if you started in the morning?), you should have your full fill. The only other way is an overfill that cools to the proper full pressure.
Packing gas into a tank generates heat, as others have pointed out, no matter where that gas comes from (bank or compressor). Pulling it out does the opposite. Easy way to demonstrate. Crack the valve open a smidge on a full tank. As the air rushes out and expands, it absorbs energy, and feels cool. Crack it wide open, and the air rushes out a LOT faster. Not only will it feel really cold, the massive heat absorption will cause condensation to start forming on the valve and eventually ice, all from the gas' ability to pull heat from the surrounding area as it expands from the compressed state. Going back into that compressed state, the opposite happens, and it dumps heat into the surrounding area (the tank). Slow the fill rate, you slow the heat generation, just like the valve went from merely cool to cold when you opened the valve to demonstrate the other side of the principal.
Pretty simple process, no physics needed when you lay it out in easy terms.