Glue to withstand high temperatures
Silicone adhesive will bond to wood and many plastics (and most things).  Most silicone will deal with high temperatures, but there is silicone designed for very high temperatures (for engine gaskets, fireplaces, etc.).  You can find it at auto supply stores, Harbor Freight, most hardware stores, etc.  Examples:


https://www.harborfreight.com/3-oz-rtv-silicone-red-90026.html
http://www.3m.com/3M/en_US/company-us/all-3m-products/~/3M-High-Temp-Black-Silicone-Gasket?N=5002385+3292638826&amp;rt=rud
https://www.permatex.com/products/gasketing/gasket-makers/permatex-high-temp-red-rtv-silicone-gasket/
https://www.amazon.com/Rutland-500-Degree-Silicone-10-3-Ounce-Cartridge/dp/B000DZBLNC