It's really hard to say without seeing exactly & with detail the placement & attachment of the lamp with respect to the "wood and mesh", but I know I wouldn't be
able to sleep until this was modified...that was a close call. She needs to find either a way to protect the wood with something that cannot burn & serves as a "heat
sink" (ceramic or metal perhaps) or use a different kind of heat source altogether (& I assume she'd still need a UV light).
When I re-purposed a large china hutch cabinet for an arboreal snake to live in, I used a heat cable (the kind sold to keep your pipes from freezing, they come in many
different lengths too) and connected it to a thermostat (the kind used for home heat...this was MANY years ago, & FYI, it worked quite well!). In that case, I ran the
cable around the sides of the enclosure horizontally, about 12" from the floor (so the snake could also be cool at the bottom if desired since heat rises -the water bowl
was also on the floor). On that cabinet, the glass in the front-opening doors did not go all the way to the bottom, so you couldn't see the cable unless the doors were
open, & even then, it didn't much detract from appearance. The cables can be also be disguised in many other ways, as long as you make sure that either the material
cannot burn, or the heat is well-regulated. (I'm thinking of a heated "branch"?) A heat lamp inside a wood cabinet would "bother me"...especially if it's not regulated.