In another place I read that a rather large amount of heat would be released when a volume of water 23,000+ feet deep and covering the entire planet was to fall. Is that correct, and if so, how did he keep the wooden boat from catching fire?
Water also has a rather large heat capacity. In fact, its specific heat of 4.186 joule/gram*K it's larger than for almost anything else around you. It can soak a LOT of heat. And it has an even higher latent heat of vaporization, if it were to come to boiling point. So I wouldn't worry much about anything catching fire.
BUT you are onto something...
But anyway, to use SI and back-of-napkin calculations, 1 kg of water can soak a little over 4000 joule to raise its temperature by 1K (or 1 celsius, they're the same for temperature differences.) 1 Joule is the work for pushing with a force of 1 Newton for 1m. Earth's gravity is almost 10 Newtons per kg.
The kilograms actually simplify out of that, since you have them both on the side of how many Newtons pull that water downwards, and on the side of how much heat capacity you have. So, lucky us.
Anyway, so you'd need to drop that water about 400m for it to go up 1 degree, assuming of course it were completely isolated. Rain for example sinks most of that energy into the air and ground.
Or you could drop it from about 40,000m (130,000 ft), to go from freezing to boiling. Of course, if it's really isolated, or enough of it to completely overwhelm any energy sinks. At first the existing water and the atmosphere would soak most of that heat. But eventually there'd be just too much kinetic energy to dissipate, and those would not do much more to keep it cool.
Now Genesis 7:11 tells us: "
on that day all the springs of the great deep burst forth, and the floodgates of the heavens were opened." Well, there isn't all that much water underground, compared to the scale of the flood, so probably most of that came from the "floodgates of the heavens", i.e., was droppend from space.
Let's say the lowest limit of LEO, or about 80 km...
Are you pondering what I'm pondering, Pinky?
Yep, that's twice the temperature needed to bring such water from freezing to boiling. Which would be the main thing that keeps temperature in check, by the end, via latent heat of vaporization. (Of course, then you'd need to pour even more water in, to reach the same altitude in spite of most of it boiling off.)
So, anyway, would I worry about the boat catching fire? No. I'd worry about Noah breathing in air at 100 degrees Celsius for the next few days. Well, for the next minute before croaking horribly, really.
ETA: Though in air completely saturated with water vapour, so perspiration doesn't help, he'd probably die of heat stroke MUCH earlier. He'd start getting hit the the really crap end of that by 40 celsius. Which is just ok, because if he survived just day more than that, temperatures would reach pain level. Full body and lung pain.