Most writers use it as a synonym for heat capacity, the ability of a body to store thermal energy.
However: The lack of a consistent definition of what property of matter thermal mass describes has led some writers to dismiss its use in building design as pseudoscience.
For example, if 250 J of heat energy is added to a copper gear with a thermal mass of 38.46 J/°C, its temperature will rise by 6.50 °C.
For discussion of why the thermal energy storage abilities of pure substances vary, see factors that affect specific heat capacity[broken anchor].
The Manual J process uses detailed measurements of a building's dimensions, construction, insulation, air-tightness, features and occupant loads, but it does not take into effect the heat capacity.
The process presumes that the building has sufficient heat capacity to maintain comfort during brief excursions outside of those extremes.