My Apple Watch suddenly got very hot and lost power

So over two years old? Battery below 80% capacity would not be unusual but let Apple analyse it.

If its just the battery its only about $80

Sounds like a battery fail.

You ought to reach out to Apple Support directly. You should be able to reach them here  Click here > Contact - Official Apple Support  or phone numbers  Click here > Contact Apple for support and service - Apple Support   or Click here > Genius Bar Reservation and Apple Support Options - Apple