Mike writes:

Some older planes had a non-compressor based system that required water. I
assume it was some sort of evaporative cooling setup. I lived in El Paso,
Texas where the temps routinely got above 43° C and I had an evaporative
cooler in my home that worked just fine.

That would be a swamp cooler rather than true air conditioning. It would work
in an aircraft if the humidity were low enough, but the weight of the
necessary water sounds like a major drawback.

You can also buy aftermarket systems that use ice.

Still not true A/C, but better than nothing.

I suppose adding a compressor to an engine would raise all sorts of issues
with certification, testing, performance, etc.