Oh , the pcie m2 adapter? I have one i used on an older board that didn't have an integrated m2 slot. The bandwidth is less though at 4x.
What do you mean? No nvme uses more than 4x lanes. So as long as you're PCIe slot for such an adapter is fast enough (PCIe version 3.0+) then there would be serious difference between mounting or in the board or using such a daughter board*.
*Actually, there might be one difference: your m.2 nvme might be using PCIe lanes that go directly to the cpu, whereas the same might not be true for all your PCIe slots - some may go through the Northbridge instead. So double check that to be sure. Tbh I don't know how big a difference in performance youll get if it goes through the NB as opposed to a direct link to the cpu, buy considering how much cooler it'll run, even naked, I'd say it's probably worth it.
The problem is your case has fans on the top and bottom, great convection helpers, but no fan is facing the pcie slots directly. So a little m.2 SSD flat up against the mobo is only getting a small amount of airflow going across it, air that mostly goes to your GPU. So yeah, even without a heatsink on it, moving the m.2 SSD to a daughter board (i like this nomenclature so I'm sticking with it) puts it directly in the path of those bottom intake fans. I'd say you'll get very noticeable improvements in its temps without even needing to buy an additional heatsink and/or fan for it.