The FJ80 utilizes 80Ws of power making it one of the most powerful on-camera Speed Lights available. This power is packaged with extremely fast recycle times which can result in a large amount of heat being produced by the unit. The FJ80 manual https://www.fjwestcott.com/amfilerating/file/download/file_id/7644 outlines the Overheating protection built into the Speed Light.
Using the maximum or near maximum output along with rapid firing exposures utilizing the fast recycle times or HSS can result in the overheating protection kicking on. This will slow the recycle time and eventually shut the FJ80 down to allow it to cool and prevent damage to the unit.
To avoid overheating, for indoor shooting at a fast pace, use a higher camera ISO setting or wider aperture if appropriate. This will allow you to set the FJ80 for a lower power level if using Manual power to minimize the heat produced. In TTL the FJ80 automatically need less power at higher ISO settings. This should allow the rapid pace without overheating the unit. Setting the zoom at the narrowest beam angle that covers the subject for both TTL and Manual operation and moving closer to the subject will also aid to keep the power level down while providing good exposures.
When possible, avoid the use of on-flash modifiers in extended high paced situations as they may restrict the ability of the unit to cool and will require higher power levels to achieve the desired exposure. When using a modifier which requires higher power settings, shoot in single shot or with a small break between bursts to allow the unit to cool.
With the FJ80, the power and pace is there to use if you need it for dozens of rapid fire frames. Lowering the output and/or slowing the pace to nearer that of a normal speed light (2.5-4 seconds) will avoid overheating in situations that require an extended numbers of frames.