I believe you meant "bed walls" or the truck's roof re: "Truck Cap". I have a 1958 8' NCO on a 1997 F350, and used 2" X 1" boards. The 1" high boards clear the bed walls by about 3/4" so the bed wall's upper rim doesn't get scratched when driving. If you have a CO version, it may be the same height adjustment, but someone else with a CO might reply with a more accurate answer.
As a side note, I secured the Alaskan to the truck bed because I have no intention of wanting to remove my 1958 Alaskan 8' NCO. I drilled through the boards, camper floor, and truck bed & frame (X 4 holes) and close the tailgate when driving. But because the extra 1" raises the camper up---it's pretty easy to open the top door with the tailgate up. So, two options:
1) EASIEST--Install one of those fence gate latches on the outside of the top door that you can paddle lock,
2) MORE WORK--If you have or add a remote lock to the tailgate (my setup), use STAINLESS STEEL screws, and add 2" to 6" wide X 1/2" to 2" "thick" piece to top of tailgate, so when the tailgate is up/closed, the top door can't be opened, but you can still see out back window on upper door when driving.. I used FOUR 5.5" x 3/4" leftover redwood fencing boards and use teak oil. I get an extra 5.5" to 22" of extra "table space" or "deck" when the tailgate is down because I used both piano hinges, heavy duty furniture hinges, and camper/trailer table folding legs.