What happens when you throw small batteries or button cells into a campfire?

As already wrote, by heat, the electrolyte begins to vaporize inside and brush the housings or can burst.

Flammable gases, such as methane, ethane or ethene, escape from the battery. Hydrogen can also be formed from the binder in the electrolyte—in combination with oxygen from the air, a mixture which is hazardous to the fire is thus formed.