I’ve built a prototype cooler using tec modules to liquid cool a human body powered from a 12-14v supply with 30A maximum, using 4 x 70W 12V modules. It works fairly well but looking at the graphs for efficiency I wonder now if using 24v modules powered from the same supply would do?
The voltage rating of a TEC is that which gives you the highest temperature difference. However, the highest COP (coefficient of performance, aka efficiency) generally comes in at somewhat less than 50% of that rating). Therefore it's likely that a 24v TEC run at 12v will give much higher efficiency than one run at its nominal rating.
Efficiency in a TEC system is critically dependent on reducing the temperature difference, so a good cold side is worth improving. Water cooling is often useful. Consider an evaporative (swamp, bong) cooler for reducing the cold side to below ambient efficiently.
There is a TEC manufacturer's site somewhere on the web that has a tool that allows you to optimise the choice of TEC and drive voltage for 'smallest TEC', or 'lowest power consumption', I don't recall whether there are other optimasation criteria. I'll try to find it and update this answer, though happy to receive comments pointing to it.
You will need at least 200W of cooling to have sufficient temperature slew rate for an active human dissipating 250W with a thermal jacket mandated by the job for other reasons.
This requires optimal liquid heat transfer for both cooling to body and heat removal to air means that your ideal supply is:
20A max 35V max 378W using ATE1-288-20AS This means the load is < 2 Ohms. But regardless of whatever TEC you choose, the TEC coolers are 0.5 to 2 Ohms so consider the P/I=V ratio first.
It doesn't mean you need to use all this power, but it must be available.
Other: If it were me, I would use only "copper sponge" heatsinks to the TEC's on both sides fanning out to the heat exchangers.
For portable use, battery load is high and TEC efficiency for COP is very, very low (<2% ??) compared to commercial A/C units (450% or a COP=4.5) or even better solar evaporation of water with pumps COP = 10 to 12. But micro-sized A/C units are very very expensive with a closed-loop thermal cycle.