It's a bit tangential to what you're asking, but for a whole tenderloin, consider searing on the grill (if you have one, weather permitting), then finishing with indirect heat in the grill, or in the oven. You'll get a much better flavor and texture on the bark, and a roast as important as a tenderloin is worth the extra trouble.
In fact, I smoke over oak first, 'til not quite rare, then sear and finish over a very hot, wood coal fire. Complex and a bit expensive, requiring a smoker. a separate grill, two oak fireplace quarter logs to make enough coals for an 8 minute sear, and the timing to make the whole thing work out -- but again, worth the extra trouble.
Whether you go sear/oven, all oven, or use one of my outdoors suggestions, don't forget to trim the tail and truss the roast into a nice, tidy package before cooking. You'll appreciate it later when you carve.