iPhone battery life short and heating up

You left out the fact that you had the battery replaced. Important information. You have a 90 day warranty on the battery, it may be failing or the power management IC may be failing. Take it back.

Go to Settings > Battery and see what processes/apps are using the highest percentage of your battery. One of them may have gone rogue. This can also happen if your router has a problem or you have a weak cell connection.

Again, take it back and describe what is happening. Genius Bar Reservation and Apple Support Options - Apple

However, before you do reset the router at your house and restart your iPhone and Watch.

Click ▷ iPhone too hot?

Click ▶︎ iPhone User Guide.

Apple won’t replace the battery until it reaches 80% capacity.

Battery Performance Tips:

• iPhone Battery and Performance.
• Maximizing Battery Life.
• About battery usage.
• Check the iPhone battery health and usage.
• Optimized Battery Charging.
• Use Low Power Mode.

Need more help?

• Call Apple Support at 1-800-APLCARE. 📞
• International Support. 🌐
• Contact Apple Support. 📝
• Chat using Messages. 💬

If it is doing it at a variety of locations and just now resetting your router, Watch and iPhone did not help I would make the Genius Bar appointment and let them test it again. There may be another issue with the iPhone.