What do you mean by interior thermo mass?
Anything you add to the heated space is added mass. Some mass will perform better than others.
Consider an empty room.
Let's say your present system on a typical day would heat that room to 70°F by 1pm and by 6pm the room is down to 65°F
Add a couch and a couple of chairs and it will now take till 1:15pm to bring the room up to 70°F but it doesn't get to 65°F till 6:15pm.
Add a half a dozen huge planters filled with water and now the room won't reach 70°F till 2:30pm, but... it doesn't reach 65° till 8:30pm.
Consider something a little different... something opposite.
Your fridge is completely empty except for that 2 year old mustard bottle
You open the door of the fridge hoping the food fairy has blessed you with a complete Thanksgiving dinner but alas... all that remains is the 2 year, 2 hour old mustard bottle. When you opened the door the fridge spilled much of it's cold air out because there isn't much mass and the temperature increased from 38°F to 42°F.
Open the door of the
'beer fridge' which is almost always stocked and full and the temperature only went up a half a degree from 38°F to 38.5°F after you grabbed a brew.
Why? The bottles of beer and their contents kept most of the cold in their mass and kept it from spilling out when you opened the door.