SSD's don't really need drive bays. Put a square of double sided mounting tape on the thing and stick it anywhere the cables will reach. They're very light, don't move/vibrate, or get hot.. so this works.
Ho Ho!- Yes SSDs do get HOT--my 500 GB SSD Runs cooking with fans ago go with a Big processing out folder.
PCIe card SSD? Out of the 4 SSD's I have (intel and crucial) I've never felt them above room temp.. even after extended benchmarking.
Maybe yours is broken and ready to burst into flames.. ;o)