Not how it works, In the natural Heat rises so what was coming back to the earth was not heated waters but waters cooled in the upper atmosphere extending thousands of miles upward and thus returning to the earth in the form of rain.
I would point out that the atmosphere is not an endless heatsink. It does have a finite cooling ability. Plus as porbably pointed out any rain coming from that high up will have an absurdly large kinetic energy such that it will vaporize and return back to its gaseous phase long before even touching the ground.
Also as pointed by wiki 3/4 of the atmospheres weight is within 11 km of the surface, and 120km is where atmospheric rentry difficulties occur. So why the heck do you have an atmosphere thousands of miles deep? Where do you get those numbers, and do you even understand what those numbers mean?
The atmosphere acts as a gigantic airconditioner, because heat rises and the bible is clear in that it rained 40 days thus the heat rose and rain returned in the form of rain, snow, for those 40 days. There was not a humidity problem because no steam problem existed during the deluge.
Are you even aware what steam is? (Gaseous water), and gasoes water exists at nearly every atmospheric temperature, and if you are talking a 25 C in a flooded world, there will be quite a bit of water present in the air.