I also have same problem and partially solved by turning mobile data off while playing game. Hot issue and rebooting problem became much less happened. I found that Xperia has pre-installed "Overheat Control" (see my post at http://talk.sonymobile.com/t5/Xperia-Z-ZL-ZR/Accidental-restart/m-p/459989#M23884) and assumed this software makes my Xperia Z rebooting frequently when playing games with mobile data switched on. I also found that Xperia has pre-installed "Crash Monitor" and believed it monitored by Sony. I do hope Sony will take action concerning hot issue and rebooting problem by using every information collected by "Crash Monitor" very soon.
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