Set up a two-zone BBQ with one side for high heat (direct) and the other for low heat (indirect). Pat the tenderloin dry and rub it all over with olive oil.
Combine the smoked paprika, garlic powder, onion powder, brown sugar, chilli powder, salt, pepper, and thyme in a small bowl.
Coat the tenderloin evenly with the seasoning blend.
Place the pork on the hot zone and sear for 2 minutes per side until a nice colour develops.
Move the tenderloin to the cool zone and close the lid. Cook for 12–18 minutes, flipping halfway through.
Brush lightly with BBQ sauce during the last 2–3 minutes of cooking.
Remove from the grill and let it rest for 5 minutes before slicing into medallions.