You can use a UTH in a wooden tank.
Either:
a. Get the right type so it can be mounted on the base of the inside of the tank. It is then covered with substrate to avoid burning. The only problem you remain open to is burrowing. You can place tiles/glass over the mat to avoid this though.
b. Mount it elsewhere in the tank. My wooden tanks have the UTH's mounted on the side wall without problems.
You can't mount a UTH on the outside of a wooden viv, it's too well insulated and no heat would transfer. Remember, as wood is a better insulator than glass, the heat radiated from a UTH is retained better in the tank than a glass viv.
I know you hear plenty people mentioning that they need belly heat, but I've heard just as many that insist it's not a requirement, including my local reptile place.
I've kept corns with side mounted heat mats for 13 years now without problems. Never had a burn and had two regurges in the whole time, both of those from a female who'd just laid eggs and was fine once she'd had a bit more time to recouperate.