unexpected change of ADC value with multiple voltage dividers (thermistors and pot)
#define meatTempPin A0
#define airTempPin A1


Your code says A0,A1 but the circuit and picture of the wires say A0,A2.  

Since A1 doesn't appear to be connected, as you scan things, the ADC could be sampling and holding some voltage from the prior conversion of potPin.

Try this instead:

#define meatTempPin A0
#define airTempPin A2