Does the drive capacity influence temperature? Not necessarily. I've got the same brand of 128GB and 256GB drive they don't run any different in temperature. Perhaps attach a heatsink if it bothers you. I've done that with harddrives I've run for long periods on hot days. I've done that even with a little drive smaller than my thumb.
On a related note, I had a little usb flash drive (verbatim) that was very hot and after I inspected it I discovered a fault on the board, an actual hotspot which didn't exist on another similar device. I promptly got my data off the drive. A few months later I plugged it in out of curiosity and the drive started to cook itself. I pulled it out and it was too hot to touch, so I promptly destroyed it. I figured the thing was going to take out my computer sooner or later anyway.