It is normal for the watch, cable and power adapter to become warm during charging.
Try restarting (or, if that doesn't work, force restarting) your Apple Watch:
Restart Apple Watch: Press and hold the side button until you see the Power Off slider; Drag the slider to turn off completely; Afterwards, press and hold the side button until you see the Apple logo.
Force restart: press and hold both the side button and Digital Crown for at least 10 seconds, until you see the Apple logo.
Ensure that you use only the recommended, genuine Apple power accessories for charging your watch.
More info: Check battery power and charge your Apple Watch - Apple Support
If you are still concerned that your watch or power accessories are not behaving normally, they may need to be checked. Contact Apple Support:
https://www.apple.com/support/watch/contact/