Do I need protection software for my MacBook Air? And how to I stop my computer from heating up after installing a malware like Cleanup your Mac.

If you already have malware such as Mac Cleanup, the following has a very good reputation: https://www.malwarebytes.com/mac/

I have never run any 3rd party virus or protection or cleanup software on my Mac. Many if not most cause more problems than they prevent. Also see: macOS - Security - Apple

In addition to the advice above, please see the user tip below to help prevent the installation of further Malware.

https://discussions.apple.com/docs/DOC-250001781