Definitely cook the tenderloins like steaks, but rarer than you like beef. If you like med rare beef, you may be able to do rare deer tenderloin
I de-bone a deer leg and put steak fat trimmings in the middle and tie into a compact shape. I do 225 with a NC-style vinegar mop till it hits 150-160m and then wrap till pullable.
The first time, I would wrap in foil as this produces a braising action.
After you do that try butcher paper and see which you prefer.
The other option would be to smoke to something like 100-110, and the direct grill over charcoal to 125 or so for a Baltimore pit beef treatment