How significant is the new iPad's heat issue? I've heard a fair bit about problems with the new iPad "overheating". However the details seem a bit shaky.

Is the increase in heat noticeable? Is it only when playing games and watching videos, or is it just from using it for extended time? 

Also, does the problem only affect some iPads, or is it a general problem (I think some components are made by different manufacturers, eg the screen)? So if you buy a new iPad, is there a chance you'll get one that heats more than it should?
Not at all. I have noticed that it is warmer when sitting for long periods (i.e. reading in iBooks, playing Hero Academy) but it is not a big deal and not even unpleasant except when the day is hot. If you look at this on a relative scale that I've just made up:

10 - 2007 MacBook Pro 17" playing World of Warcraft
9 - Hell
8 - Dave's Insanity Sauce
7 - Chili con carne
6 - cup of coffee
5 - iPhone 4 in Personal Hotspot mode
4 - cup of coffee when you remember to drink the last bit
3 - New iPad
2 - Old iPad
1 - Fonzie


You get some more perspective.