Will it damage my iPad if I use an iPhone charger to charge it?
No 

I mix and match my chargers often, the only disadvantage is that the iPhone charger charges slower according to a lot of sources, but I have yet to experience it. I still have an iPhone 3G charger I use as a spare at work to charge my iPad on occasion.

Interestingly I have never noticed my chargers getting hot either, but will admit I have never actively looked.

Looking at the Charging Tips here the reason for the slower charge is that the iPhone charger is 5W compared to 10W for the iPad, based on wattage alone, I can't see how you would damage the iPad, I would suspect using a higher wattage might however.