Turn switch on power lights come on when you turn thermostat up power goes out

Year make and model ?
Did you check for power at the brake light switch ?

The brake light wire leaves the brake switch and goes into the turn signal switch. They often share the same wire: the rear turn signals and the brake lights. When turning, that side is routed through the turn flasher, but you get a steady brake light on the other side.
So you have power to the brake switch. Pull apart the connector for the turn signal switch, and see if you have power in on the brake wire (with brake depressed of course) going into the turn switch. If you have power in, plug the connector together, and see if you can backprobe the connector with test light or voltmeter, looking for power out to the rear brake lights. If power in, but no power out, the turn switch is probably bad.

Since power from the brake light switch goes thru the turn signal switch, have you checked the turn signal switch for power in and out on each circuit ?

Do you have power in and out of the brake and turn signal switches ?
Power goes into the brake switch, then to the turn signal switch, then to the light bulbs.

I assume the fuse has power if the hazards work.
The third brake light skips the turn signal switch, the regular brake light circuit goes thru the turn signal switch.
Do you have power going into the turn signal switch on the red lite green wire from the brake switch ?

Do you have power at both sides of the brake switch when the brake is applied? If so it sounds like the turn signal switch is bad. try turning on and off the 4 ways a few times. sometimes this will clean the connections and it will start working.
The power goes through the fuse to the brake switch. from the brake switch to the turn signal switch from the turn signal switch to the tail lights. If the 4 ways are on the power goes through the 4 way fuse to the 4 way flashers then to both sides.
If the turn signal is on and the brake is on, the turn switch cansles the power from the brake and uses power from a 3 fuse and flasher for the side that the turn signal is called for.
If I typed to fast let me know. I can answer any questions you might have.
If this helped you please vote 4 thumbs up. :-)
good Luck and God Bless

one wire is 12 volt power all the time weather the key is on or not, the other wire goes to the turn signal switch on most models, ( you did not give your year or model ) , if the car uses the rear turn signals as brake lights also then the wire goes threw the turn signal switch, if the car has a separate turn signal bulb in the rear ( usely has amber lens in the rear ) then the second wire from the brake light switch goes to the BCM ( body control module ) and the BCM turns the brake lights on.

This is a common GM specific problem. Your turn signal switch contains an elaborate networking device that has to cancel brakelights while running a turn light. Often times the ground within the turn signal switch is lost causing your situation. After investigating such other possibilities as fuses and loose grounds it may become necessary to replace the turn signal switch. Thank you, Dana

Does the turn signals or hazards work in the rear?? Yes... it may be the brake switch or the turn signal switch (power goes from battery, to the brake switch then to the turn signal switch, then to the lights. No? .. again.. possibly turn signal switch or the wiring between cab and bed.