130-140 degrees internal will yield medium rare to medium. For rare you want the internal temp to be 120-125 degrees. I take mine to right about five degrees less, foil and rest for at least 15 minutes. The internal temp will continue to rise to the target temperature.
Your Brinkmann should operate at about 250 degrees so make sure your thermometer batteries are good and keep an eye on it. If it isn't too big it will hit rare between one and two hours, medium rare in two to three and medium just under three and a half hours.