I barbeque my turkeys by first splitting them down the breast into equal halves. This helps them cook faster and more evenly. Marinate the meat in whatever spices you like. Place the turkey on a grill and cook until a thermometer placed in the thigh reaches a temperature of about 150 degrees. Pull the bird off the grill, cover, and allow to rest for about 30 minutes or until the temperature reads 160 degrees.