Hey ilyangski,
Thank you for using the Apple Support Communities! We understand your iPhone 13 Pro appears to be getting warmer than expected. We'd like to help.
Based on the description of it getting warmer than expected when transferring files and while connected to the charger, those can be expected reasons why the device would feel warmer. If you're performing intense tasks, it will feel warmer too. There are several more reasons where the phone getting warmer than expected are considered normal. Check out this article please: Keeping iPhone, iPad, and iPod touch within acceptable operating temperatures
"When you use the device or charge the battery, the device might get warm. You might notice that your device feels warmer in these situations:
- When you set up your device the first time
- When you restore from a backup
- When apps reindex or reanalyze data, like Photos tagging for faces, places, or keywords after a software update
- When you use graphics-intensive or augmented-reality apps or features
These conditions are normal, and your device will return to a regular temperature when complete.
Here are some of the higher ambient-temperature conditions and activities that might cause the device to change performance and behavior:
- Leaving the device in a car on a hot day.
- Leaving the device in direct sunlight for an extended period of time.
- Using certain features in hot conditions or direct sunlight for an extended period of time, such as GPS tracking or navigation in a car, playing a graphics-intensive game, or using augmented-reality apps."
We also invite you to review the section in that article titled 'If your device gets too warm' and 'If you see a temperature warning screen'.
Best regards.