Strain Gauge - Wheatstone bridge DRIFT
You may be seeing thermal EMFs, as well as thermal drift of the resistors. 

Blowing hot air with a hot air gun is not the way to test a circuit like that. Use a proper environmental chamber with a fan inside and control the air flow over the board (maybe with a bit of foam). You may have to wait an hour or two for the temperature to stabilize. The hot air gun will lead to wrong conclusions. You may see dynamic changes that even out as the gradients disappear. 

Do not have anything on the board that dissipates a lot of power (I assume you are doing this). 

Leaded resistors can be a bit less prone to change from external mechanical forces. Try flexing the board a bit and see if your reading changes. Chances are this is not your problem, but it's worth a check.