Battery Message and overheating

Hi

I have brought an IPhone SE 2nd Gen in excellect condition from backmarket 2 or 3 days ago and ever since then its been over heating and showing a message saying unknown part (Battery) and it dies way quicker than my other Iphone SE 2nd gen i brought from another seller from Backmarket. the overheating can also really really heat up but this ive seen 1 or 2 times. It can also overheat when its Idling.

Apple says bring the IPhone in for repair for £65.

Backmarket has a 1 year warrenty on there stuff but i dont trust them to send my Phone beacuse of icloud putting my data on there

Whats the best option?