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I have an old Mac Mini 2014. The fan goes on the moment the system powers up, and it never goes off. What are some possible issues for me to check?

Does the fan shut off once you shut the machine down? You may want to check it for dust build up. My brother in law’s PS4 was running hot and the fan was extremely loud until he removed the case, cleaned out the dust and sprayed compressed air throughout the console and it works fine now.

Your system is in CPU’s Safe Mode as one or more sensors believes the system is in trouble! Besides pumping the fan’s RPM it will also lower the CPU’s clocking. Try running the onboard diagnostics. Restart you’re system and press the D key. Did you get any errors? Reference: Mac startup key combinations