If you are worried about the mat getting wet then there are a couple of options.The first one is to cover the heatmat with a peice of perspex and stick it down with tape or silicone.T^he second is to mount the heatmat on the back wall of the viv.
I have my heat pads under my vivs.I put little rubber feet on the viv that lift the viv by about 1-2cm (get them in b&q,homebase) so you get a good circulation so you wont get problems with your heat mat.
All my mats are attached on the under side of the viv so you get a good amount of heat getting to the viv and good circulation under the pad.In my 3ft viv i have a 12" wide heat mat.
I've got a couple of vivs with mats under false floors - I leave a gap of about 5mm above the mat.
I used 3mm laminated hardboard for mine, but I reckon perspex would be a better bet.
One thing though - if the royal is currently in a viv with a bulb I'd keep it that way. A mat in a viv won't raise the ambient temp much at all - a degree or two if you're lucky - not enough for a royal. (May be the same with the carpet - never kept them so not sure.)
Kings/corns/rats should all be fine as long as the room temps aren't really low.