Cooking a small boneless ribeye roast

It's not that I can't find info on cooking a rib roast on these boards, it's that there's way too much info to wade through. I've got a 3.25 boneless ribeye roast that I want to cook for New Years day. Right now, I'm thinking season today and leave in the fridge uncovered overnight, remove from the fridge and leave at room temp for an hour or so, roast at 500° for 20 minutes, then shut off oven and leave for two hours. I prefer medium-rare to medium, my hubby prefers well-done. I can easily throw his in some jus if it's not quite done enough for him, but I absolutely don't want to overcook the thing. Anyone have some good experience in cooking a similar roast?