I have one wooden viv with the rest melamine (so effectively plastic-coated wood).
I use the UTH either underneath the viv, sat in a recess in a double layer of cork mat made from cork wall tiles(to stop the weight of the viv resting on it), or inside the viv, covered with ceramic wall tiles (just laid loose over it, not glued down). When inside the viv, I add some extra shielding for the part where the wire meets the mat, as this is most susceptible to poop spills which might cause it to short out.
I prefer them outside the viv wherever possible because of the risk of damage to the mat (and therefore the snake!). The heat comes through the floor with no trouble, it just needs the thermostat probe to be measuring the floor temp inside the viv immedialtely above it.
I've seen custom-made wooden vivs with false floors, where the UTH slips underneath the false floor but rests on the actual viv floor. It's a rather nice solution if you can manage it, preventing the snake or its output from coming into contact with the UTH.