iPhone 5 Blue Screen Crash, any advice?

My iPhone 5 was working perfectly fine last week. I would frequently use Kik messenger and have no problems using it. While messenging over Kik, my iPhone screen dimmed significantly and locked up completely. No home button, lock button, or touch screen function would respond. Sometimes the phone would bluescreen, others I would just hard reset it to have the same problem occur. This also happens playing videos on Safari or upon pressing the send button on facebook messenger. After the blue screen, my iPhone would get hot with minimal usage and battery life from 100%-0% is around 45min to an hour. The lady clarified that iPhones tend to get hot when they do some work and I told her that the phone was idling with no apps open and getting hot for absolutely no reason. This was not a problem before the bluescreen.

This also happens when opening "voice control" by holding the home button... definitely not the app's fault.

I have done the following:

Restored as a new device;

Put in DFU mode and restored that way;

Updated to the latest iOS;

Taken it to the genius bar. They tried to say it's the app's fault, but I demonstrated that the issue did not manifest itself on Kik using other phones on display, they ignored that and told me that it's the app's fault.

I no longer have this under warranty and I certainly do not want to pay the $269 replacement fee as I cannot afford it.

Hoping that this is an issue I can fix.

Thanks,

Adam.

*EDIT*: Can confirm the problem happens on iOS 7.1 as well.