its not just a PITA its a PITFA to get right.
It can be done tho, and it can also be more efficient then a phase change unit if you have the proper setup, like you run overpowered TEC's at its highest CoP, and then use a PWM on them so they pulse instead of constantly gobble electricity.
It also helps to have them cool water, and then have the water pumped to a cpu block as the holding potential in water will prevent less of a loss if insulated right. It also helps to have them a thermometer so they turn off @ certain temp and then back on once temp exceeds X degree's, this way you can avoid condensation. For example i had my TEC's turn off when water temp reached 10C, and then kick back on again when water temp reached 13C. This left my window of 3C in which water temp could be held at, and condensation does not occur @ 10C, unless its ridiculously hot outside, and you have a high humidity index.
The beauty in tec's is that they can be shut off, and then turned on rapidly, unlike a compressor which requires a cooldown period between each run, hence if your really milking the CoP it can be more efficient then a phase system.
However, again... PITFA....
I think my TEC setup honestly only lasted 2 weeks tops before i shelf'd it because it was so terribly inefficient.
RIP:
it had 5 Tec's on that chiller, required 2 loops (hot / cold) side, where the hotside was cooled by 2 massive 480's.