My MacBook Air seems to overheat and turn the loud fan on a lot

The past week when I power on my computer it gives me an error message saying I shut my computer down because of a problem and would I like to open the apps I had opened? When I did not shut it down because of a problem and all my apps were already closed. Then this morning on the log-in screen half the screen was grey and only a sliver on the side showed my background photo. I tried restarting my computer, updating the software, and force quitting finder but nothing seems to resolve these issues.

This is probably unrelated, but it seems to overheat and turn the loud fan on a lot when I'm doing small tasks on applications like Word, PowerPoint, and Safari and have to exit out of the application for it to cool down again.

Thanks to anyone that has any suggestions!

[Re-Titled by Moderator]