It opens up some interesting tactical possibilities. Sending in a whole bunch of small decoys and cheap missiles, forcing the enemy to overheat their guns taking them out or risk taking incremental damage from lots of small impacts, or using decoys to mask the real threat.
Perhaps the rate of cooling might depend on how close the fight was to the nearest star. You'd have squadrons manoeuvring for "the sunward gauge" in the same way that 18th century fleets tried to get the windward gauge. With the enemy forced to fight with their turrets facing the star, their guns would bleed heat more slowly. You might even get larger ships trying for battles in interstellar space while small ships would try to engage close to stars where the battle-wagons' fire power would be limited.
Sooo many ideas and possibilities ! 😁