"Thermal mass is most useful in locations that have large swings of temperature from day to night, such as desert climates. Even if the thermal mass does not prevent heat energy from flowing into or out of occupied spaces, like insulation would, it can slow the heat flow so much that it helps people's comfort rather than causing discomfort."
Heavy or massive objects like masonry can help improve thermal comfort as well as reduce peak heating and cooling demands in buildings. They need to be designed into buildings such that they can charge and discharge thermal energy which often requires a temperature different between the thermal mass and their surroundings. On exterior walls, they work best when coupled with insulation. They, by themselves, are not good insulators.