Marinated Grilled Steak. The proper temperature to cook a medium-rare steak is 130° - 135° F. Although, according to foodsafety.gov, beef, lamb, and pork should be cooked to at least 145° (or above, if desired).Ground meat must be cooked to at least 160° F. Ground poultry must be cooked to at least 165°.arinated Grilled Steak. The proper temperature to cook a medium-rare steak is 130° - 135° F. Although, according to foodsafety.gov, beef, lamb, and pork should be cooked to at least 145° (or above, if desired).