I've recently partially reverse-engineered a similar display board for a wine chiller that sounds pretty much identical to what you've described.
That board uses the NTC pin to output what looks to just be a square wave (90Hz, constant 75% duty cycle). The resistance between that output and ground is what's used to determine the measured temperature, so I think your guess of a current being measured might be right, but it's the current through the negative thermal coefficient thermistor located on the cold side of the thermoelectric element, not the element itself. I haven't looked at how the current/resistance measurement is implemented. It looks like there might be an opamp and other support-circuitry on the power board in the back that's also involved.
The PWM output pin confusingly doesn't output PWM, but just a constant 5V or 0V, depending on how the temperature measurement compares to the set-point. The power board in the back does have some circuitry with a TL494 that's generating PWM output for the fans. I wonder if perhaps it's named like that because it's one of the inputs to the PWM circuitry in the back.