1 After 20 minutes of high heat cooking reduce heat to 350Â°F and continue to roast for 1 hour to 1 hour and 15 minutes OR until the meat thermometer reads 130Â°F for rare doneness OR 140Â°F for medium-rare doneness, that is the way a prime rib really should be served, check your roast after 1 hour cooking time. *NOTE* if desired you can cover the roast loosely with foil the first hour and then uncover and cook for the remaining time. --------------------------------------------. 2  APPROXIMATE COOKING TIMES for the prime rib cooked at 350Â°F after the 20 minute cooking time at 450Â°F. 3  Rare; cook 12-13 minutes per pound or to 130Â°F.