Proper header size for a 10 foot span, non load-bearing wall
You don't need a header, except to provide a "space" for your new overhead door to roll-up into. A header is to hold something "up". This is non-bearing, so you could use studs to create the space down from the roof (or ceiling) for the roll-up door to roll-up into. The load that you need to resist is the horizontal force on the "wall" above the new door. I'd use a double 2x6 laid flat at the head of the opening. (The door is not supported by the "header" either.) 

I'd use 2-2x4 "jack studs"...just for stiffness on each side of the opening. (Technically, I guess they're not "jack studs".)