A beef roast cooked to medium-rare should have an internal temperature of 145°F - 150ºF after the resting period, and a roast cooked to medium should have an internal temperature of 150°F to 160ºF. (See the note below). See Beef Doneness for more information on proper cooking temperatures.hen roasting beef it is important to select the proper cut of roast beef to produce moist and tender meat when the roast beef is cooked to the desired doneness. Using the proper beef cooking times and temperatures is critical to the end results.