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Where are you saving the pictures? Internal or external SD?
That's an odd behavior, how do you know is the camera creating this heat?
It could be another app or apps and since your phone gets hot, it will lower the screen brightness and disable the camera to protect the phone.
What I would do is to boot on safe mode and check again.
http://talk.sonymobile.com/t5/FAQ/How-to-boot-your-phone-into-safe-mode/m-p/348008#U348008
Just try my suggestion, boot on safe mode > let it cool down > while on safe mode use the camera and report back.