Tiling behind a wood pellet stove

I am about to tile behind a free standing wood pellet stove, and want to know if I have to use cement backer board, even though there is already sheet rock behind the stove. The stove is within code even if I left the wall the way it is, but I want to know if I'm going to have problems with expansion in the grout lines where the wall will be warming up and cooling down frequently during the winter. Any help would be greatly appreciated-I'm pretty new to tiling.

Should be fine tiling directly over the drywall.

Use modified thinset mortar. The dry powder you mix with water.

DO NOT use Mastic tile adhesive. The premixed adhesive that comes in a bucket.