The battery housing is not in direct contact with the outer mouse cover. Because of that you might need to repeat the heating procedure a couple of times to loosen the battery adhesive enough in order to remove the battery.

Heat an iOpener and apply it to the back of the mouse.

A hair dryer or heat gun may also be used, but be careful not to overheat the battery as it is susceptible to heat damage.

At higher temperatures the plastic mouse cover becomes heat sensitive. Avoid overheating it.