As with any product.. there are always going to be some with issues that slip thru the cracks. If I just bought a new iPhone and within 24 hours having issues.. I would not send it in for servicing.. I'd just return it.
When you say the volume won't increase.. are you saying the button doesn't work? Or it just doesn't go loud enough for you?
Have you made sure that the iPhone iOS is up to date? current version is 13.6
Update your iPhone, iPad, or iPod touch - Apple Support
Charging your iPhone can make it pretty warm.
There are settings in the iPhone that can cause it to be quite warm.. ie if you are allowing background activity. There is all kinds of info and tips on the internet about ways to help your battery life. Just google iPhone getting hot