PC Blue Screens and then instantly reboots. How do I stop this or find the error later?

Quickest thing to do is go in to Control Panel > System (Windows Key+Pause/Break) and then under Advanced, you should see "Startup and recovery", click Settings and you can disable Automatic restart on system failure.

Next time a BSOD occurs, you can see what the cause is.

FYI - A CPU fan failure is very unlikely to cause a BSOD, it would simply cause a thermal error on the motherboard and an instant shutdown.

Also, you may want to see BlueScreenView, a very good tool to help you see previous Blue screen errors.

Note: This procedure is the same for Win XP, Vista and 7

Open the System Properties window, and move to the Advanced tab.

In the Start up and Recovery section, click the Advanced button.

Within the System Failure section, uncheck the Automatically Restart option.

Tutorial: Debug Memory Dumps (Figure out what is causing a BSOD)

I tend to favour whocrashed for post BSOD analysis. Sure there's more direct ways, but this tends to do all the heavy lifting for you.