None of the outside components get nearly warm enough to present any danger of flamibility to anything. I have accidently left plastic baggies on top of mine and there's not even a sign of distortion in shape let alone melting. A wood cabinet will be no problem.
Ps - have you seen the CookShack Shack built by BBQ Rod, a member of this forum? It really is a thing of beaury! Take a look:
http://forum.cookshackamerica.com/cgi-bin/ultimatebb.cg...t_topic;f=1;t=000953 Welcome to the forum Frank!!! Let us hear about that first smoke.