Can I insulate between a brick chimney and drywall?
If there is a straight open space accessible from above, you might consider  polyisocyanurate foam insulation. A 2 inch board has R-13 insulation.

You might want to consider a wireless thermostat.  There are numerous types (both proprietary and wifi) that would allow you to move the sensor elswhere even if the base station was on the heated wall.