The best way to increase the thickness of the triceps is by growing the lateral head. Heavy press lockout variations are key here.
The bench press, decline bench press, and overhead press are good choices for working the lockout position. Just set up the safety pins in the power rack so that you only have to press about 8-10 inches in the exercises. The lateral head responds best to heavy loading and these are the exercises that allow you to load the triceps with the most resistance.