There's always a little rust on the caliper piston. If you can reccess the piston easily with a lever than the piston is free. Your anlysis of the hot rotor does imply a stuck caliper though. If the caliper is dragging it will warp the rotor. You may have an air bubble or water in the brake fluid causing the caliper not to retract. Have you bled the brake lines?

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2013 X5 3.5i M Sport
2004 M3 cabriolet SMG