installed Catalina the battery drains quickly and the laptop heats up.

Use Activity Monitor to Kill Runaway Processes

     Use Activity Monitor on your Mac

     Runaway applications can shorten battery runtime, affect performance, and increase heat and fan activity.

Should the above not prove helpful, then make an appointment at the Apple Genius Bar for service. If you need to find an Apple Store - Find a Store - Apple.

You might try reinstalling Catalina:

Reinstall El Capitan or Later Without Erasing Drive

Please be sure you back up, if possible.

1. Restart the computer. Immediately, at or before the chime, hold down the Command and R keys until the Apple logo and progress bar appear. Wait until the Utility Menu appears.
2. Select Disk Utility and click on the Continue button.
3. Select the indented (usually, Macintosh HD) volume entry from the side list.
4. Click on the First Aid button in Disk Utility's toolbar. Wait until the Done button activates, then click on it.
5. Quit Disk Utility and return to the Utility Menu.
6. Select Install OS X and click on the Continue button.