Overheating of the IPhone 13 pro

My experience says this is purely caused by some third-party app that you may have installed.

I am not aware of the ambient temperature in which you are using the iPhone. However --> Keeping iPhone, iPad, and iPod touch within acceptable ...

Store the device where the temperature is between -20º and 45º C (-4º to 113º F). Don’t leave the device in your car, because temperatures in parked cars can exceed this range.

Use iOS devices where the ambient temperature is between 0º and 35º C (32º to 95º F). Low- or high-temperature conditions might cause the device to change its behavior to regulate its temperature. Using an iOS device in very cold conditions outside of its operating range might temporarily shorten battery life and could cause the device to turn off. Battery life will return to normal when you bring the device back to higher ambient temperatures. Using an iOS device in very hot conditions can permanently shorten battery life.

I too had a similar issue few months ago on my iPhone 12 Pro bought two years ago from Apple Store in the USA.

What I did is given below

1. Took a backup on iCloud (Which I do regularly)
2. Logged out of the Apple ID
3. Erase --> Erase iPhone - Apple Support (IN)
   1. Keep eSIM Data was the option I chose (See the pic)
   2. .
4. Set up my iPhone and restored it from iCloud Backup
5. 

I continued to have the same issue with the heating.

I repeated the above steps but this time I did not restore from the iCloud Backup. I set it up as a new iPhone.

Waited... There is no heating issue.

Conclusion.:

• This does not suggest any hardware issue!
• This is also not an iOS issue
• Some Apps or iPhone storage maybe heating up the device.
• This is not the iPhone Cover or Charging able issue as I had used the same cover and cable while doing both the above processes

Action Plan:

• I will now slowly get my all data back one by one.
• Using the elimination process I will try to find out which app or settings were causing this...

It has been many months since then I have got back 70% of my apps and the heating issue has not returned. Probably the rogue apps were not used now.

Just go to Settings > Battery option and find out which application is consuming more battery power. Try to close or uninstall that app and monitor if the issue remains as it is. if issue is resolved, then reinstall back that removed app and monitor the battery power and heating issue. If overheating issue continues, report the app developer for the same.