Leave it a little rare in the center. Cousin Mark and I are often conflicted about our tuna, because in the summertime, my friend Jack catches Yellowfin tuna, and I get it while the rigor mortis is still evident, the most certain sign of freshness. I will give you my Cousin Mark's recipe for broiled Tuna with Three Mustards. Jack likes his smoked, and we often have a Smoked Tuna Salad Nicoise as a luncheon buffet platter. For broiling, a little further from the fire, lift the grill or if you can, lower the flame or let the coals get grayer.
Most people use charcoal too soon anyway.
The coals should be ash-coated. When I worked a fish grill in a restaurant, I would mark the fish on the grill to get those nice criss-cross grill marks, color it well and then finish it on a heavy aluminum plate in the top of the broiler or oven. If you have a double grill, just grill for color and markings, and then move it over to the side that's not on, and close the cover to finish. This is a good technique to use when you have a large number of people to serve at once. F or baking frozen fish, double the suggested cooking time for fresh, but lower the oven temperature a little.