I’ve used essentially the same method when there was 3 feet of snow on the deck. You do want to let it come to room temp first. The food nazis will say that’s unsafe but I’ve never had any problem. Time depends on thickness of steak. I like mine rare and a relatively thin steak at room temp may be done after searing. The sear and pat of butter on top are probably the two most needed qualities to produce a restaurant quality steak. I pat the steak dry but don’t salt and pepper it until after brushing it with olive oil right before putting it in the pan. Another critical component is letting it rest on the counter covered with foil for about 5 minutes after it comes out of the oven. In that 5 minutes you can deglaze the pan with some red wine, add some herbs and butter, reduce it slightly, add salt and pepper and have a nice sauce for your steak.
Mark