that does sound like the thermal protection kicking in
but can you check the battery voltage with a multimeter when it has dimmed down .
the light only needs 10 ish volts to run properly and the battery should never get down that low
lowest it should get is 13 volts so it may be some cells have given up under load but are recovering when resting
I can check out the light head for you. but you would need to get Smudge to check the battery and charger
to discharge fully set the light up outside and make sure there is a good airflow over it and leave on til it dies then check the voltage you might need to briefly connect the charger to restet the protection circuit
one other thoughtbis the driver circuit has become detachedfrom the heatsink this would explain the light being cool when it happens