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I smoke mine at 180 over night and turn up the temp to about 250 when I wake and pull mine at 140 and wrap in foil. I used to cook them on my wood BBQ with the adjustable grate using only oak but them come out great on the smoker too.
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.
I smoke lots of these tasty little morsels. Like the rest of the nice folks here, I take mine to 145 and foil it in a warm oven for 30 min. Has always produced a great product!! Here is a thread if you want to see the finished product. http://www.smokingmeatforums.com/for...ad.php?t=83603