Share your experience!
1. Try a different charger or cable
2. What happen when you lock the screen?
3. do you have a protective case or film?
Things to try
1. Boot on safe mode
http://talk.sonymobile.com/t5/FAQ/How-to-boot-your-phone-into-safe-mode/m-p/348008#U348008
2. if the problems persist you could, repair with PCC or Bridge
Bridge (for Mac)
Alternatives on How to backup Xperias
http://talk.sonymobile.com/thread/36355
3. If neither 1 nor 2 work then contact your local Xperia Care