Not cheap, but there are third-party monoblocks (like
this one) for the R5E10.
Aside from the processor (and GPU cards, etc) the only parts which
require cooling would be the PCH and VRMs. Other stuff - "SB", RAM, M.2/SSD, etc - could benefit from dedicated cooling (especially if they're running overclocks or high duty cycle) but they don't strictly require it. You could always use heatsink/fans if you have enough through-chassis airflow, but you'll find things a bit tight and crowdy around the VRMs. There's no reason you can't use an AIO cooler, but finding one which fits can be problematic. Another option is TEC coolers, great at spot cooling but less efficient overall, and sub-ambient cooling can introduce other complications (like liquid condensation). And yet another option is to fab your own heatpipes/coolers, or transplant them from some other board, though it might look kinda ghetto.
Your most affordable option might be a used R5E10 mobo off eBay, you might be able to buy a "dead" board cheap and the only things on it which really need to work are the parts you intend to salvage.
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[/Korth]