I totally agree with letting meat come to room temperature before cooking. It will cook much more evenly. When I grill steaks, I pat them dry, put a generous amount of coarse sea salt on both sides, and let them sit out until they come to room temp. They sweat out a small amount of moisture. Then pat dry again, season both sides, and grill. Somehow the salting alters the surface and you get much better browning. And the room temp lets you get a good medium or medium rare throughout, instead of overdone outside and a raw, bloody middle.
I like ribeye, but I've never seen this monster cowboy thing. Is that what Fred Flintstone tossed on his car and knocked it over? When I was in Italy a few years ago, I wanted a Tuscan Steak. You pay by the weight, and the smallest was over a kilo, about 2.5 pounds! My wife and I split it and had leftovers the next day. It's like a 3" thick t-bone. They don't ask how you want it cooked. It comes pretty rare, and I'm pretty sure it's just seasoned with salt, and then some olive oil after it's cooked. It was great!