Early 2011 MacBook Pro CPU problem?

Is this what you see at startup?

Prohibitory symbol



A circle with a line or slash through it means that the selected startup disk contains a Mac operating system, but it's not a macOS that your Mac can use. You should reinstall macOS on that disk.

Then follow the instructions:

[I]t means that the selected startup disk contains a Mac operating system, but it's not a macOS that your Mac can use. You should reinstall macOS on that disk.

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.

That repeating pattern could be something "phoning home." When you ran Activity Monitor it was set to list "My Processes." That can miss some potential culprits. Use the "view" setting to change this to "All Processes."

This time look at the list of processes. That may help spot an offending process. To my the cyclic nature of the problem is more suggestive of a software issue than a hardware fault.