It must not overheat..
Try to perform a software repair , but if the problem persists even after repair then you must get it checked at service center
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Backup everything as it will erase all data on phone (sms, contacts,apps)
Update/Repair your phone via PCC or SUS
PCC (PC COMPANION) – Repair your software with this .First do the setup without connecting your mobile to pc.(only connect when you are asked to).
Do it as follow >> PCC > SUPPORT ZONE> SOFTWARE UPDATE> REPAIR SOFTWARE (written with blue)
PC Companion http://www.sonymobile.com/global-en/tools/pc-companion/
SUS ( Sony Update Service) ... download and install it on pc and follow the on-screen instructions http://www-support-downloads.sonymobile.com/Software%20Downloads/Update_Service_Setup-2.11.12.5.exe
or
http://www.sonymobile.com/global-en/tools/update-service/
Both the links are same
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