Dear WG,
I don't recall "thermal mass" being a formally defined term. As Butelja tells us, it is a term that describes the quantity of heat in a body. I don't think it needs precise defining, but rather competent useage of the term.
Sometimes you might use it to refer to the amount of heat stored in a body, in which case you have to include the body's temperature with reference to some datum, such as ambient. Then, your term would be calculated by mass*heat capacity*temp difference.
It's not "thermal diffusivity". By that I think you might mean conductivity, or perhaps, heat transfer rate.
Does that help?
Cheers,
John.