Les,
My limited knowledge of Peltier devices come from having to sit through a bunch tender proposals for heating/cooling solution for remote servers. I was a system architect on a networking project for the cargo branch of a european airline. The project involved installing and remotely maintaining a server at each cargo destination across EMEA. Several of the servers at the smaller, more remote airfields where installed in what were little more than corrugated iron shacks, which meant they could either get very hot in summer or very cold in winter. The chosen solution was a peltier device as it could serve both purposes .
The heat tube ran from the server enclosure down to a large aluminium plate buried a few feet under ground where it was colder than ambient in summer and warmer in winter. That system used a thermister. I don't know any more details.
But a word of caution: There is discussion (in the otther forum) of undoing the silicon sealed bolts shown left and right in this image:
I believe the 3rd central silicone cover labelled with a ? above, is the valve used to inject the refrigarent into the system under pressure (to make it liquid), and the silicone seals are there to prevent leaks. If the bolts are undone, the liquid will escape as gas.
My gut tells me that it is the board that is at fault, and the peltier unit and cooling matix should be left well alone. Besides the gas leak problem, peltier devices are famously physically fragile.
Perhaps the simplest way to check the peltier device would be to use a 12V battery (car, bike) to drive the PD direct and see if a differential temperature develops between the input and output pipes. However, I don't know enough about PDs to know if they require a current limit supply.