Well, being full of hot air is debatable. While the outside air temperature was rising, it was also in constant contact with the cooler water. But I guess the inflation monitor (basically a small ruler that measures 10 centimeters to compare to a stamp on the boat that expands as it inflates) was showing that the boat had expanded more when we were all done, so I'd say slightly warmed air.

Better to be a smartass than to play along with that stupid joke

No idea how far to field of dreams, I think I only saw that movie once and don't remember where it was :P