Try this , put it in the freezer for couple of minutes around 25 minutes until the whole body gets really cold and then charge it until something pops in the screen .
If it doesn't turn on after 10min being charge, turn it on by pressing hold on the power botton .
if it doesn't turn on , keep it charged and press down the home botton and the power botton together until it turns on .
If it doesn't work , keep trying , you have nothing to lose .
My phone died suddenly while it was on 90% battery when I was in a hot country for vacation and I did this and it work just fine after . I freezed it and charged it . The body and interior has probably gone through over heat since iphone is made of metal and because it is a electronic device.
Cheers
-Nicole