Unheated slab and flooring install/home heating question

A homeowner with a concrete slab foundation (a solid slab poured on the ground, insulated underneath and along its edges with rigid foam) wrote in with a question about how the slab affects heating. He's found that the slab's mass acts like a thermal battery: it keeps the house cool in summer and holds warmth well in winter, so he can leave his wood stove off on the coldest days and lose only 5 to 10 degrees over 24 hours. The trouble shows up in fall and spring, when outdoor temperatures swing between the upper 30s and low 60s. During those seasons the house tends to settle at 60 degrees. He can light the stove and warm it to 68, but by morning it has dropped back to 60 just as fast. He burns less wood overall than neighbors with similar-sized houses, but he has to start fires earlier in the season than he'd like, and his family notices the chill.

Now that he's about to install hardwood flooring over the slab, he's asking whether adding a layer of foam insulation under the new floor would help or hurt. His question is whether foam would separate the living space from the slab's temperature-stabilizing mass in a way that works in his favor, or whether it would just as easily cut the house off from the stove's heat and make the swings worse. It's a useful example for anyone with a slab-on-grade home: the same thermal mass that smooths out extreme winter and summer temperatures can make the shoulder seasons feel harder to control, and flooring choices sit right at the center of that tradeoff.