Start looking for a GFI that is tripped. Look in the garage, utility room, laundry area, bathroom, etc, etc. Look behind boxes, stored items. For a house of that era that is the most likely.

You really need to start from the outlets that don't work and go backwards from there. You need to find where the power for them is fed from and see where the power is lost.
It could be a loose connection somewhere between the recpt and the panel cb.
The thermostat may or may not be part of the problem. Is it line or low voltage? Usually any heat would have its own 20a circuit.