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hi,
What temperature ranges are you working with, also how many squares and how big.??
E.
15 to 35 C would mean you have to cool them as well as heat them. Do you need that. It would be much easier to just heat them.
Pour some current through some power resistors. Make the squares out of aluminium, attach the resistor, and use PWM to control the temp to balance out the heat loss due to surface area of the squares
If you need to cool them below ambient as well as heat them the peltiers are probably the answer. I keep trying to talk you out of cooling them because it will add a lot of cost and complexity.
I think I would start out with an aluminum plate the size of the board as a heatsink. Then peltiers and the small metal squares. I would use some type of insulator for the white squares - maybe pcb material.
I think I would use two PC power supplies for the peltiers so you would have a + and - 12 volt supply. If we are on the right track we can talk about temperature control.