Here's an interesting problem, with what I hope you'll find to be an interesting solution. One can find nice, modest TEC controllers with current source outputs, attractive units with digital readouts and IEEE-488 interfaces, etc., available for low prices on eBay. I say modest, because these controllers might be able to provide only up to 4A max with a 4V compliance. It would be appealing to beef up these controllers to say 100W, or 10A at 10V, etc.
If a simple 2.5x current multiplier were available, then an ordinary power supply could provide the power, while the low-power unit provided computer control of the TEC- driven temperature and digital readouts.
Here's my candidate 2.5x current multiplier / booster:
. INPUT x2.5 current booster, 10A max out . CURRENT . o--, IRL2505 ,------o -- TEC ---o . | Q4 | . | |--' | . +-----+-----+-------||