I decided on using a TEC, as I have no familiarity with using them, and condensers can be loud, which is unappealing. The noise from a fan is acceptable. I don't need it to be large, and a simple cooler associated with shipping chemicals should be more than sufficient. The 3cm thick walls realistically should provide enough insulation to allow the TEC to get it cold. Of course, as the cooling is a function of the air temperature (e.g. if an ideal 40°C gradient, the cold side could get below zero), if the room temperature is too warm the cooling effect will not be significant.
A standard ATX PSU is being used to supply power to the fan and the TEC, as the 12V *rail* can provide as much as 22A. The TEC can handle as much as 200W, but for safety concerns, I'll limit the TEC to 100W, and see the results. Currently with my benchtop supply, 36W (12V, 3A) does not provide much for cooling, maybe 3-4°C below room temperature.
For the temperature display, I decided to go archaic and not use any MCU for an A->D converter to display. I will be using a comparator network with closely matched resistors, and display the current temperature in C on 2 7 segment displays, and 1 LED to indicate negative (although I do not expect to drop below freezing).