IMHO, deer meat / venison really can't be cooked over medium rare and maintain good flavor, tenderness or moisture. I 99% of the time grill on the BBQ at a very hot temp, my go to is marinade in olive oil and garlic pepper seasonings. I use a gallon zip-lok to marinade in and toss it around a little for a couple hours. The olive oil will help retain moisture and give your meat some good color from the grill. The trick is a HOT grill and no more than MEDIUM RARE ........