Tempereature of flash is not a problem. Sometimes I see sign “Overheating” and got to wait 1-2 minutes. Most of time I shooting 1\125-1\250 exposure of flash. So it’s overheating few times per working day (5-6 hours). And I use 1 battery for all day.
But If I use exposure of flash = 1 it will overheat often and I need 3-4 battery for full working day.