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That's normal if you are syncing multiple accounts and/o auto updating apps and/or auto backup your photos/videos. Also, the phone can't overheat, if it gets too hot it will shut down.
Hi
It's normal for android phones to get warm when using mobile data.
However make sure the phone doesn't get heated a lot ( so that it becomes uncomfortable to hold) or that could be a problem. If you feel there's a problem, kindly have your phone examined at Sony service center and they should be able to help you with it.
EDIT : Lol uli, looks like we both are sitting next to each other. Unfortunately no auto refresh available