Is a Curie pendulum an example of a heat engine?

Just like it takes work to pull a book vertically off a table, it takes work to pull a piece of iron off a magnet. If we weren't heating the metal, but just had a hand pull it off the magnet, you could easily see where energy was being used to do work. (In fact, we could hook up a small pump to harvest some of that energy).

After you pull the magnet away, you've increased the magnetic potential energy of the system. You get the energy back by letting them approach again.

Although you don't see the hand do it, the same work has to be done (in this case by the thermal energy) to move the iron away from the magnet. It's done by rearranging the magnetic domains instead of by pushing the iron away, but work is done nevertheless. This work rearranges the magnetic field and increases the magnetic potential energy of the system.

Without seeing the field lines rearrange, it's easy to miss this work. An analogy might be boiling a pot of water. Cool, all the water is in the lowest gravitational potential energy state of the bottom of the pan. Boiling moves the water higher into the room. When the water cools, it falls back to the bottom. You could make a (very inefficient) engine that works by allowing the condensed water to fall through a water wheel as it cools.

It is a heat engine. There are two isothermal energy transfer stages, a high temperature heating stage by the candle at the burning temperature while the metal is still ferromagnetic, then there is a cooling stage during which the metal releases thermal energy to the air (environment) and in between work could be extracted. Check the magnetocaloric phenomena [1], it is widely used though in the reverse cycle, that is as a cooler not as an engine.

[1] https://en.wikipedia.org/wiki/Magnetic_refrigeration