if the screen replaced recently, you can check if the black tape is still on the blacklight contacts. if not maybe that's your problem, because this could in fact create a short circuit and make the phone really hot.
check on the new screen if there is no dust/hair on the connectors, after that test the screen again. if you still have this problem you've a faulty screen
maybe it's a software issue and not a hardware issue. you can try to press home button and power button on the same time for 15 secs. after that the phone will be reboot and maybe that will fix your problem.