I don’t see what you’re disagreeing with. As you and I have both said, there is no heat created .
While it is not strictly in conformance with thermodynamic laws, I think of temperature as “heat density”, and heat itself as “packets”. In a volume of air, say 1 liter, at some given temperature, the heat packets would be evenly distribute thoroughout. Compress that volume and you’d reduce the volume but retain the same number of “packets”, increasing its density, thus raising the temperature. Blow ambient temperature air over that newly hotter volume and you’ll cool it. Allow it then to expand and the “energy density” will lower, hence the lower temperature.
This will always, as I’ve said, be relative to ambient temperature. Since the entire process never starts with anything absolute, but only with ambient, which is of course relative.
And I’m pretty sure there’s no "d’ in refrigerant.