In a ring-on-a-shaft situation, when you apply heat the outside component expands more than the inner one even if you heat them both to the same temperature and they are made from the same material. The reason is that the increase of diameter of the inner component is proportional to the material's bulk coefficient of thermal expansion, and the increase of diameter of the outer component is proportional to the material's linear coefficient of thermal expansion, which is always greater. If you want to convince yourself of this, just find or make a steel ball, and a steel ring which very nearly drops over the outside of the ball but not quite. Put them both in an oven with a glass panel in the door, and heat them. When they get hot, the ring will drop over the ball onto the oven shelf they are both standing on. That used to be a demonstration of the principle involved, used in school science lessons.
Of course in practice you apply the torch only to the outer component anyway, so the difference in expansion is even greater.
Please keep us posted on this project Nick, if possible with pictures. A lot of members are interested in bringing old ride-ons back to life, so this will be useful for the archives.