When plugging into sync, the charge icon flashes on and off onrepeat

Basically. This is a sad day for the iPad; I woke up to find it had slipped down the side of my bed and next the radiator; a very hot radiator.

It displayed the temperature cooldown icon, and I quickly cooled it down. it was there for too long, maybe an hour when the heating was turned on.

Now, the battery seems to be at whatever it was before in % but I tried to plug it into the laptop and it quickly had an issue. The charging bit on the top left of the screen, flashes in and out of the green charging bar and the little lightning icon, repeatedly and indefinitely.

I can charge it (thank god), but I also can't back it up; my other main concern.

i have hard reset it, but restoring it i can't see making much of a help. am i doomed?