Hey rumeet,
It appears that you're having a couple of issues after updating your iPhone 13 Pro Max to iOS 15.3.1. It's getting warmer than it used to and the battery life isn't lasting. We're glad to glad to provide assistance.
If your iPhone, iPad, or iPod touch gets too hot or too cold - Apple Support -- Review the information provided in this article for the advice Apple provides when your device is getting warmer than expected.
iPhone Battery and Performance - Apple Support -- This article has great information about the battery of your iPhone.
About the battery usage on your iPhone, iPad, and iPod touch - Apple Support -- Use the steps in this article to determine which apps have been using the most power for the past 24 hours and last 10 days. Either take screenshots of what you've found or note which ones are using the most and save the information for later.
Batteries - Maximizing Performance - Apple -- After reviewing the information under "General Performance Tips", go to "Tips for iPhone, iPad and iPod touch. Apply any of the tips provided and review the battery usage after a few days of applying those tips. Compare what you're finding now to what you found earlier to see if there's any improvement.
About Optimized Battery Charging on your iPhone - Apple Support -- This article applies more to the battery health you learned about in "iPhone Battery and Performance" above. To help your battery last longer, we recommend using Optimized Battery Charging.
Feel free to get back to us with any questions or problems you may have.
All the best.