4 Cover the grill and cook until the temperature of the interior of the tri-tip reaches 120°F for a rare roast, 130°F for medium-rare and 140°F for medium. At this point the meat will take anywhere from 20 to 40 minutes to cook, depending on how hot your grill is, how well done you want it, and the size of the cut. 1 tri-tip roast, also known as triangle steak, a bottom sirloin cut (anywhere from 2 1/2 pounds to 4 pounds), look for one well-marbled with fat.