Hi Jürgen
As the support articles explain, Apple Watch and the charger are expected to become warm during charging. If necessary, Apple Watch will also regulate its internal temperature.
The battery is designed to retain up to 80% of its original capacity at 1,000 complete charge cycles. The One Year Limited Warranty includes service coverage for a defective battery.
However, if you are still concerned you can and should contact Apple Support by phone (you have 90 days of complimentary phone support) and ask for their advice:
https://www.apple.com/support/contact/
If you are still concerned after that, you can book an appointment at an Apple Store to have your watch checked.