So I purchased this new Xperia V today, updated to last firmware 9.1.A.1.140, but when I do stuff on the phone even when not too CPU demanding, it heats up very much, and I mean really heated up, near the camera flash... What could be wrong?
That is most likely where the battery is located. I don't know what your definition of "not too CPU demanding" but i know when i use my Galaxy nexus for extended lengths of time it heats up noticeably over where the battery is. Even when the screen is not actually on and i am not interacting with it, it can heat up due to processes and services going on in the background such as email sync or music playback or social site syncing. This could be part of what is going on with you. Also, when I charge it it heats up. There probably is not anything "wrong" with it, just a lot of stuff running. If it makes you feel better, when it starts to heat up, turn it off and take out the battery until it cools down, then put it back in.
Try system updates (if available). Usually company fixes these kind of problems in them. Else close all the unwanted apps n restrict them from starting up again
Switch off your phone when you are not using.
Lock your phone when it's not working.
Don't run too many apps in same time.
Don't use the phone while it's charging.
Don't play games or watch videos when it's getting overheated.
And I have to tell you something... I have an Xperia V.