Robert,
I apologize given I misread your first post, thought the air units were fine....my mistake, sorry I sent you looking for a small breaker box in the bay.
Fred asked the right question, there must be a 12V fuse or resettable breaker that feeds the thermostat circuit along with the awning. Maybe someone knows where that might be. I am puzzled about the awning given mine works on 120V but maybe yours is powered by 12V and has a common fuse. That would make sense given that the motor on the awning was being used, which would be a larger load then any thermostat, current wise. When the fuse blew it killed power to all three items being on a common circuit. So I would look behind the switch panel that runs the awning and in your manual to see if it mentions that fuse location. Maybe someone knows and can post that info or a call to Ken at Bend.
If you wanted to be sure about the air units getting 120V you could go to your main 120V breaker panel, pull the cover and measure the output side of the air conditioner breakers to ground and confirm 120V. There is no real need to do this given your failure mode, all other 120V circuits are working and the 120V for the airs come from separate 120V legs. The legs are fine given all other things are working and the chances of two 120V breakers failing together is zero.
If a plus 12V source is near your thermostat and a wire could be temporarily run, you could locate the 12V feed wire on the thermostat, remove it, and use a temporary 12v wire to power up your thermostat to get cooling until that fuse can be found.
Later Ed