I agree that local dirt is much cheaper than trucked-in construction sand, but I think my design sketch above shows that a "sand battery" whose only moving parts are fans will be about 30× cheaper than a real battery at household scale, even though the sand is still most of the estimated cost. A "sand battery" designed to power a steam turbine is a much more difficult problem to solve, but in this case the stated problem is just that it's 24°F (-3°) outside, so I think much cheaper solutions are fine, with no pressure vessels, stainless steel, insulated silos, sand conveyors, or heat transfer fluids other than garden-variety air.

Do you have a good handle on the pressure (and therefore power) requirements for getting air to flow upward through sand? I feel like you ought to be able to get a pretty decent amount of thermal power out of half a tonne of sand with a really minimal amount of pumping, but that's only a gut feeling. Definitely as you go to graded-granulometry gravel the required head drops off to almost nothing.

Thanks for the link to the Olds device! That's utterly astounding. Archimedes could have used it for raising sand, although making a sturdy enough tube out of wood might have been a bit of a chore.