Does the iPad Air stay cooler whilst charging than the previous iPad? My iPad 4 gets quite hot whilst charging, even without a case. As I get this with every one of my iOS devices, as well as Macs, I always expect this from a device now.

However, the iPad Air is much thinner than the previous iPad, and consequently has this had any impact on the temperature of the iPad Air whilst charging?
Yes, the airs will be cooler than the 4th generation iPads when charging due to the laws of physics. How much cooler may be hard to estimate and simple to test empirically once we have shipping devices and a thermal imaging camera.

The specifications of the iPad Air show that the surface area of the back is 40,680 mm^2 (169.5 x 240 mm) and that it contains a 32.4 watt-hour battery.

The specifications of the 4th generation iPad show that the surface area of the back is 42,934 mm^2 (185.7 x 241.2 mm) and that it contains a 42.5 watt-hour battery.

So, to charge the Air you have far less energy (ratio of 1 : 0.76) going in to the device and only a slightly less (ration of 1 : 0.95) surface area with which to dissipate heat from the charging of the battery.

Since Apple almost always limits the charge rate of it's devices to get 80% of the full charge in 2 hours and the remaining 20% and top off in the next 2 hours we can safely expect that pattern to hold. Since the energy going into the older device isn't offset with enough extra surface area to dissipate that heat - the lesser energy going into the Air during an recharge cycle will let it's surface temperature run cooler to dissipate all the heat that the battery puts off while charging. I also see no reason to think there will be less or more airflow from speaker openings and such or that the glass of the Air will insulate more or less than the previous generation.

So I can confidently predict the iPad Air is going to be cooler than it's predecessor in more ways than one.