Why does my iPhone 5S get hot, goes to a blue screen, and then reboots?

[iMore Question]

When i switch on my iPhone 5s it seems to get hot it works fine for a while then a blue screen comes up then it reboots , works for a while then does the same again. It is on ios 8.2.
also I set up the finger print scanner it let me do that and completely but when I try to use it it does nothing and have to open with my screen lock code
any ideas what the problem is nd how to fix it.
It's out of apple warranty now so apple shop prices are a no no.
Thanks for reading

 

[kch50428]

also I set up the finger print scanner it let me do that and completely but when I try to use it it does nothing and have to open with my screen lock code

You have to enter the unlock code after device restarts...

As to the rest - if you don't have AppleCare+ you're out of luck if you're not willing to go to an authorized service provider...