jim rozen writes:

I think what you were saying was, that there could be
*two* things going on in the regulator at one time.
The first being expansion of the gas, which causes
it to cool. The second being the friction or turbulence
inside the regulator, which causes the gas to heat.

Yes.

In the extreme, I imagine if you ran an air motor into a brake, powered by
a can of boiling liquid freon, you would wind up with a lower temperature,
yet more heat.