Hilsch Tube for Cabin Temp control...

And small, unpressurized airplanes don't need cooling. The air outside
is plenty cold. For heat, there's lots to be had from the exhaust or
oil with a simple heat exchanger.

In a pressurized airplane, I don't think the vortex tube would work. I
don't think you can exhaust the cold side into the cabin and the hot
side overboard, so I think you're back to conventional AC.