Here's the theoretical answer, because any real-world answer runs up against questions of what the manufacturers are actually doing today.
If you change from a 4s pack to a 5s pack and you adjust the per-cell capacity down by a factor of 4/5 to match the 5/4 increase in voltage, you'll keep the total pack energy the same.
Assuming that your ESC and motor efficiencies remain largely the same, the increased voltage means your current will go down by a factor of 4/5.
So your capacity will have dropped by 20%, your current will have dropped by 20%, and -- all else being equal -- your battery heating will remain the same.
Only if you go to higher "C" rated batteries, or keep the same cell capacity (thus making your pack 20% heavier), will you pull less current compared to the cell's "C" rating -- so I wouldn't anticipate less heating. If anything, unless you go to a 2 + 3 pair of packs with airflow in between, I would expect that you'd see worse cooling rather than better.
If someone was running 5s packs and they were running cooler, it was either because (a) the batteries had better real-world discharge performance than yours did (and manufacturers "C" ratings vary wildly. I can't quite say they're all lies, but I wouldn't depend on them much), or (b) they had better cooling than you did.
A higher cell count will probably result in lower dissipation from the ESC, if its power loss is more conductive than from switching losses (switched amplifiers, like ESCs, suffer from switching losses that go by voltage). But maybe not (I'd believe what Castle or Shultzi, and probably Jeti, says on this, but not any Chinese ESC manufacturer).
So I wouldn't expect a change from 4s to 5s to drive a change in pack temperature to any extent other than any other random battery change would. It may do other good things, but to drive the pack temperature down I'd go for better cooling, and maybe buy higher "C" rated batteries from the same manufacturer, or look around for a different manufacturer with a more conservative "C" rating.