XT3 unxepected shutdown during photo shoot

[Bcndude]

Recently I had a three hour studio strobe photo shoot, this was the first time I was using the XT3 for the whole shoot, everything went fine but about 2.5 hours into the shoot the camera just shutdown suddenly, I did notice it was a little hot, but not so hot to shut down, of course I almost panicked to death, I even had the (hopefully false) impression that something was burning. I turned it off, changed batteries although the one in camera (fuji original) was still half way full and waited a few minutes, camera worked fine for 2 minutes, shutdown again, waited, turned on, worked ok so at this point every time the model changed I turned the camera off. This shouldnt happen... logic says this was overheating, but for a photo shoot? this camera is brand new. Any advice or suggestions? This almost ruined the day, never ever happened before to me with other brands. 

Thanks! 

[Rainer_Buddy]

If after 2.5 hrs of shooting the battery is only used half-way, that is strange in the first place.

I always take a second body with me for shootings. Highly recommended. (And I'm not a pro.)