It may take a bit of meddling, but I could see that heater working in the vivarium. Yes it will need a cover so that the snake cannot come into contact with it and burn itself (something along the lines of chicken wire will work). I can't tell you whether or not it will be enough heat by itself, but try it out, if you want. Setting up any enclosure takes a certain amount of experimentation.
There's no way you'll be able to use a heat mat with the enclosure, but I could see other types of UTHs working. How thick is the bottom of the viv? Depending, some flexwatt with a thermostat could work (as long as you elevate the bottom to allow airflow), though I might worry about fire hazards if the wood is very thick.
As snakes are nocturnal, they do not need any source of "sunlight" (UVA/B radiation).
Good luck, and have fun! If you have any other questions, that's what we're here for.![]()