What do I do if my ducted heating fan won't turn off?

There are a few issues that can cause this, and diagnosing the one relevant to you will require an examination from a qualified technician.

This is most likely an electrical issue; for a short term fix, you can cut power to the fan from its outlet. This is unlikely to solve the problem as the fan will start-up again when power is restored; however, it will rest the unit while you wait for proper repair.