I've done it with smaller crabs collected from rock pools. An adult however is going to need a pretty large set up....and tbh, i'd imagine most are pretty stressed by the time you see them at the fishmongers awaiting the pot.
They are fine if you have a decent water volume and provide plenty of food. Tidal pools are subject to large variations in temperature so they can survive at 20C or above even provided that it's not constant. I'd certainly keep it out of direct sunlight.
I also kept sea anemones for some time in the same set up and a decent community of zooplankton was still present after a good 10 weeks.
I would stress however, my attempt wasa deliberate short run, for a full time year round set up, i'd go for at least some sort of cooling. My mate Chad (Widmer - the reason I add the name is because you should buy his book, it's on amazon, haha) used to run cables into a small reservoir through a small freezer that he'd drilled holes in to cool the water for his jellies.