alphacat92:
I connected the positive side of the TEM (thermoelectric module) to Vin+ on the INA219 and the negative side to GND. I also connected Vin- to GND.
The INA219 is mainly a high-side sensor.
The input voltage(s) shouldn't get 'below ground', which is possible the way you have connected it.
Better to have VCC as a reference point.
If you connect the Peltier to the two inputs of the INA, then you short out the Peltier with the buildin 0.1ohm current sense resisor, and you only measure short circuit current.
If you connect the Peltier between V-in(-) and ground, then you can read open voltage of the Peltier. Make sure votage only goes positive.
Can't measure both at the same time, unless you use the Peltier as a power source, with a suitable resistive load.
Must AFAIK have several hundred degrees C across a Peltier for some power generation.
The one you linked to can't do more than +50C.
Leo..