No Follow. Medium rare prime rib ‚ that is, meat that is mostly pink with a deeper, nearly red center, is cooked to about 130-135°F. At 120-125°F the meat is rare, and at 140-145°F, it is well done.You should know the USDA recommends cooking beef to a minimum of 145°F.how Image. Medium rare prime rib ‚ that is, meat that is mostly pink with a deeper, nearly red center, is cooked to about 130-135°F. At 120-125°F the meat is rare, and at 140-145°F, it is well done.