Increasing the thermal mass of a component under an already stable thermal servo system will not make the thermal system more accurate, it will just increase the thermal settling time, and increase the heater overshoot when the system is slewing, reaching set-point. The whole point of a thermal servo system is to eliminate external factors, so rather than adding thermal mass, I think it'd be better to add thermal isolation so that the servo system will not have to respond as greatly to external thermal inputs, either thermal sources or conduction paths to other devices.
It's good to think of what could be done to the basic IC to improve its deployment, but adding thermal mass is not something I'd consider along those lines.