After having used the new iPad for over a week and performing a few tests, I've found that it's noticeably warmer to the touch than the previous generations of iPads, but could not be considered "hot" - it isn't uncomfortable to touch or hold.
I found that even though I don't currently have an active Verizon plan, turning off the cellular connectivity (Settings --> Cellular Data --> Cellular Data OFF) reduced the heating to nothing during normal activities (reading, web use, email, simple games). It feels about room temperature when the LTE cellular chipset is off.
The heat would go up slightly for very graphically intense games, but not to the degree that it increased just having the cellular connection on.
As power efficient as the LTE chipset is, it still consumes significant power, even when not actively transmitting data, and that power results in additional heat. Consider turning it off for those times you know you're going to be in an area with wifi, when you need the battery to last longer, or when you are concerned about the extra warmth.
The heating is entirely within the operating temperature range of all the iPad components and humans, so it will not damage the iPad, nor burn anyone under normal use.