Can the frame of a solar sail be made with shape-memory metals to contract in a way to maintain orientation to the Sun either in orbit or interplanetary? Would there be enough temperature difference from being in or out of the shadow of the sail or distance from the Sun to use memory metal this way?
Shape memory allows generally only change shape once during a heating cycle and need external force to deform them. The much older bimetallic structures or wax motors would probably work better for something intended to cycle repeatedly.
In answering the original question the answer is 'probably', the question is if the added mass from the physically quite large structures needed to stabilise the sail with low torque actuators would be better than systems electrically controlled by your on board computer.
You will still need computer controlled systems since this sun driven control method will only maintain two of the three axis, and cannot detect motion. So asymmetry producing lateral thrust and correction of thrust with respect to the sun pointing axis would need to be under some other form of control to get a thrust in the direction of travel rather than just out from the sun.
If your aim is to throw trillions of cheap objects out of the solar system in random directions this would work, but they would be leave on very inefficient trajectories so be traveling very slowly (and potentially end up just hovering in the Oort cloud rather than truly escaping), and the control system would tend to make them avoid any stars they did randomly run into.