Charger is overheating on a refurbished device I purchased. Battery?

Finger Lakes Fishing how hot is to hot and you did not tell us if your phone charges or what happens when the charger gets to hot. Anyhow since it happens on multiple chargers I suggest that you contact the seller and see what got refurbished. Make sure they are reputable and if so consider exchanging it. After all, refurbished devices should still be functional. If for whatever reason you cannot do this, yes, I would go ahead with a new battery. Also, get a USB ammeter and see what amperage your phone pulls. This could be an indication that there are issue with the charging circuit. In that case a new daughter board should fix this. Something like this video will help you with that.

All lithium battery chargers are current-limited. It seems unlikely to me that the battery would be able to overheat the charger. But of course there are many other current sinks in there. I like oldturkey's charger circuit. Not that it matters much, you'll want a return/exchange in any event.