There'a maneuver called a "BBQ roll" where you basically set the craft to doing a barrel roll in order to prevent any one side from overheating. I image that could help some.

IIRC during transit you'd want as much mass between you and the Sun (as shielding), and as small of a cross section facing the Sun. Probably also to reduce heat reaching the propellants.

So in a cylindrical ship you'd want to have one end pointing at the Sun most of the trip. This is, of course, very different in effect on the hull compared to the repeated expansion and contraction of heating cycles.

That's not necessarily true. Even spaceships in LEO will perform temperature-driven rolls so as to distribute heat and radiation. I have to assume that long-term ships like interplanetary transport will do the same.