Might work. I'm convinced I've felt that change in some of my used shoes with just body heat. But they may be too far gone. Wyatt and Dad redid insoles and of course cork and outsoles in a pair of 1970s AE Tulanes for me. I love em.
Yeah, if the dude before you was super fat, he is going to have compressed the cork so much it might be hard to change things.
What I was thinking of is something like a hot, wet towel, and then stand in them while they're still wet, then allow to dry.
I honestly do not know if this would be wise or not. Generally I try to avoid putting wet into shoes.