Combine the rub ingredients (garlic, thyme and salt) in a bowl.
Rinse and pat dry the tuna steaks. Place on a work surface.
Sprinkle some of the rub over one side of the tuna, and gently rub it into the fish. Turn the tuna steaks over, and repeat. Let the tuna rest with the rub for a few minutes.
Coat the grill with the oil spray. Then place the tuna on the grill. Grill covered on direct heat for 90 seconds. Turn the tuna over, grill for another 90 seconds or so for medium rare tuna. Remove the tuna from the grill, and place on a platter.
Cut the tuna steaks into thin slices, about 1/4 an inch. Plate several strips of tuna along with your side dish, and enjoy!