iPhone 4S running hot and short since Exchange update

No issues with my 4S. Are you sure there isn't some rogue app running?

May I suggest a backup and restore? Or, maybe a trip to the local Apple store. Wow! Look at me rhyme, I'm a poet and i didn't even know it!

Could've fried an egg off my precious

I found my 4s completely powered down and scalding to the touch two nights ago, after little usage - except I did have a few apps (maybe around 10 running in the background - this has never caused a problem before.)
Freaked out, but was able to recharge it the next day - no problem or heating. Decided to delete some photos before backing it up and was browsing when it stopped working after maybe an hour suddenly and it seemed to get hotter once it had stopped.
However, I had not updated to 6.1 - just IOS 6.
When the phone cooled down I started it up, turned off the apps, backed it up and upgraded to 6.2 and it seems to be okay so far...

my mums has started doing this, has anyone figured out what the problem is?

I'd suggest a full restore.

Turning it off and back on will stop any rouge process. Nothing functioning normally should make the phone act like that. Some things that can are apps that sync data get "stuck" trying to send or receive. Same with e-mail (including webmail, not just Exchange). The expectations are that turning your phone off/on will stop the rouge process and the phone will behave normally until the same process starts again. More often then not it doesn't happen again. However, sometimes you have to find and delete / reinstall the app. There are lots of utilities out there that will let you see the running processes to find what is pegging your CPU. Good luck!

try resetting the network settings

DFU + restore as NEW, don't use backups.