I have to take a picture every second or two. So for sure the flash device will build up some heat.
What about the external flash that you will be firing? Won't you have the same heat problem there?
Yes, but an external flash is bigger. So it is easier to add some fan cooling for the relevant parts. Second a bigger device could run at lower power, while it is designed for higher power. A builtin flash has to run at full power because it is so small.
For example the Yonguo YN560 could run without heat problems at 1/4th of the max power.