Air Conditioning - What powers thermostat?

A friend had a A/C failure and asked me to come over and take a look and be there when A/C Tech arrived which would be a short time later. I have some vintage experience as a A/C tech that dates back to the early 70's. As I checked for the obvious, battery failure in thermostat I realized it was not powered by batteries. I looked inside air handler cabinet, which he had already opened for a transformer but the thermostat leads seemed to spliced though out to the condensing unit? At that point the Tech arrived diagnosed the trouble and he found a short in the condenser wiring from I'm assuming vibration because the wiring was secured to the piping @ that point. In the course of a very nice conversation I had forgotten to ask him before he left. He said the drain safety switch was also fried as a result of this short and the machine trying to start with it there. He did a great job diagnosing & repairing the problem(very fast) but now I'm left with question of thermostat power? Any thoughts?:confused:

what kind of thermostat? digital programmable? If yes, 24 volts from the transformer powers it.

what kind of thermostat? digital programmable? If yes, 24 volts from the transformer powers it.

It's Carrier puron split unit w/digital programmable thermostat.
My question is where is the transformer located in the condenser cabinet outside?
I have a Trane unit that batteries power the VisionPRO Honeywell thermostat

on most systems the transformer is in the furnace or air handler