I had this problem with my 5S (never my 5). It seemed to be related to heat?.. when I had my local hotspot, iTunes, etc, running. The device would get reall

I had this problem with my 5S (never my 5). It seemed to be related to heat?.. when I had my local hotspot, iTunes, etc, running. The device would get really hot and then shutdown. When it was cool enough, I could reboot it. When I took it to the Apple store, they guy was like 'yeah, this happens to mine too'. He was cool though, he gave me a new one. Have no idea why it was happening.. if it was a heat issue, then I would have expected it to happen sooner (I had the S for about two months).