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If The Heat point is near camera???that is normal,if this not this may be a battery problem...contact sony service beacuse u can get warranty of 6 months for battery.....
No one can answer that question, there are myriad things to take into account, network coverage, is it poor, is it stable, are you using wifi, how many apps are you running in the background, how many accounts are you syncing, brightness, etc etc