I've had my BV7000 Pro for about six months and recently it seemed like the battery overheated a little. But since then the battery drains completely three times per day with I've turned off everything!
What's the deal? Can I fix this somehow?

you could test if its a hardware issue or software issue.
software issue may be fixed through flashing the latest firmware and make a factory reset after that.

If it is a hardware issue it can maybe get fixed by changing the battery. you can
- change it by yourself
- go to a local repair store with the new battery for geting help
- ask your seller for help in warranty time