Hmm... The info I found indicated you want to simulate the temperature AND moisture conditions the seeds would see naturally. Therefor the slightly damp but not wet river-sand. But, you have top prevent mold.
(River sand because it is so fine and then easily sifted away from seeds, once the sand dries.)
That said, I can try our unheated shed, too. Just have to use containers the occasional mouse can’t get into, as our cats are too lazy to catch most of ‘em.
“have to prevent...”
Paul you didn’t mention a state where you live. I put my envelopes of seeds in those white containers that dried french onions come in. I have over a dozen and they label nicely with a marker. Separate ones for lettuce and radish,
tomatoes, etc.