Prepare the grill to high temperature, 425°-450° and make sure to set up two temperature zones. Clean the grill grate well and close the grill lid to preheat.
Mix together the BBQ sauce, maple syrup, and cayenne pepper. Divide in two to brush some on before grilling and some during.
Pat salmon fillets dry with a paper towel and season each fillet with salt and pepper on all sides.
Rub the skin with oil and brush the other three sides with BBQ sauce mixture.
Place each salmon fillet on the grill skin side down over direct heat and close the lid. Let it cook about 6-8 minutes. Check on the salmon to see if you need to move it over to the cool side if the skin is getting dark too fast.
If you need to, move it over to the cool side, brush with some more BBQ sauce mixture, and cook another 3-4 minutes. To check if salmon is done, you can either touch the top to feel the firmness of the flesh or use a meat thermometer.
To use a meat thermometer to measure the internal temperature, check the thickest part of the fish. Take salmon off the grill when it reaches 135° at the thickest part and let it rest. (USDA recommends salmon safe temperature to be 145° but some people feel that it is overdone.)