A practical approach might involve placing the PCs in a closed cabinet (insulated if it's metal) with the PC PSUs and the peltier power supply on the outside of the cabinet.
The peltier(s) mounted to thermally-isolated heatsink(s) (isolated from the cabinet walls, if metal) on/thru an external surface of the cabinet would need to be able to exceed/extract the heating capacity of the CPUs and memory sticks, mainly, without the added heat load of the PSUs.
The PC case fans would likely provide adequate internal air circulation if the cabinet's internal dimensions are reasonable (not excessively oversized).
Got a small/medium sized refrigerator?
Liquid cooled CPU heatsinks have been around for quite a few years. One problem might be condensation of humidity if the heatsink is cool.