A heat engine based on rubber bands

Just to elaborate on @Adrian Howard answer, the heated rubber bands on the left side of the wheel contract, pulling the left side of the rim closer to the bearing and the right side moving further away from the bearing (assumes the rim is rigid and does not deform). In order for the rim to move to the right while the bearing remains in place, the cooler rubber bands on the right have to stretch. The net result is the center of mass of the wheel shifts to the right of the original center of mass.

The figures below may help to visualize what is happening.

The wheel at the top is not heated and therefore the center of mass of the wheel is at the center of the bearing.

The lower left figure shows the shift of the rim of the wheel to the right of the bearing due to the contraction of the rubber bands on the left (causing stretching of the rubber bands on the right).

The lower right figure shows how the shift in center of mass of the wheel to the right creates a clockwise torque about the bearing causing the wheel to rotate.

Hope this helps

The hotter, tighter bands will pull the steel rim off center, so the rim will be pulled to the right in your diagram, making the right side heavier.