What adhesive to use when tiling the fireplace hearth?
I have tiled many areas around wood stoves. It’s not only the adhesive but the tile, backer board and air gap that all come together. I normally use thin set with an admix. It is tougher to keep in place until set but I have had mastic melt several years later and the tiles start slipping down. 

The gap I mention helps the backer board radiate heat so the tiles do not get overheated. With a wood stove your stack should not be getting above 350-400 (500 is getting close to problems). When I used to install free standing we always left a magnetic temp indicator that showed the stack temp. A single wall stack to the ceiling kept below 500 should do fine with thinset. 

If mastic is used keep the stack temp lower or it may melt and the tiles will start slipping down and falling off.