iPhone 12 Pro Battery Over heating problem?

When you are streaming music, watching videos or doing anything really which uses more power, the battery works harder and when a battery works harder, it generates heat. This is normal and should be the case with ALL iPhones, past or present. What they shouldn't do however, is get so hot it's uncomfortable to hold in your hand. Your phone has circuitry designed to alert to overheating and actually shut the phone down if the heat reaches a level too high.

So, warm is OK. Too hot to hold is not. Your phone comes with a one year warranty, but If you think the battery is generating too much heat, schedule an appointment at your Apple Store Genius Bar for evaluation and if Apple determines it is not operating normally, they will replace it.

On a final note, if you have just set the new phone up in the last day or two (likely since you just received the phone), it may still be indexing data, which depending on how much data you had to migrate, could take a couple of days. I would give the phone a few days before doing anything.