Phone heats up and drains battery fast when Cellular Data is On

My family is taking a trip across the US from Maine to California when my wife's iPhone 4s - Verizon network - Page Plus service, began to drain the battery fast and get so hot that it would give a warning message and shut down. This had never happened before. I tried shutting off Location Services and background apps, but noting seemed to work. She was running iOS 7.1, so I backed up her phone and did a complete reset where the iphone was completely erased. The problem was still happening. I did a network rest and nothing changed, besides the phone now saying that it could not activate. I upgraded her iOS to 8.1, but no changes.

I discovered that if I turned off the Cellular Data, the overheating problem went away. But, now the phone is not activating and says I need to call Verizon. More network resets do not change this condition.

The wifi seems to work fine, as well as everything else on the phone, except the Cellular data.

I'm not sure if there is some weird network thing that kicked it off, since it is a Page Plus phone, or if some hardware feature decided to break on us.

I have the same iphone 4s, with page plus with no issues at all.

Any ideas of how to start troubleshooting this issue?

Thanks!