Great report, but if you had to add a external fan, that suggests something more sinister or happily fixable at home is at play. The system is designed to shut down if it gets too hot.
The System Management Controller, SMC is, among other things, responsible for hardware systems that cool your Mac. An SMC reset is easy and often overcomes cooling issues. Instruction here, note you need the method for an Intel Mac:
Reset the SMC of your Mac - Apple Support
If that does not change things, run Apple Diagnostics. It is very good and spotting problems with heat-related hardware, specifically important sensors and fan motors. More reading:
Use Apple Diagnostics to test your Mac - Apple Support
If it throws a code, there is a link to the decoder page at the bottom of the above page I linked.
Your Mac breathes in cooling air through vents across the entire bottom edge of the display. You must maintain that ~3 inches of clearance between the vents and the work surface. A chap who was having serious heating issues including shutdowns like yours, posted this image of his iMac on its workstation. I added the red highlight:
When I worked in law enforcement, we called tha a "clue!"
Hot air must escape and it does so through a smallish vent under the neck of the stand near the RAM door:
This is usually not a problem but I had a real workout with one overheating complaint. We'd been through every step above except the venting. I asked if a vent could be blocked. He said no, the iMac was mounted above his eye line so had a huge amount of free space for the intakes.
When I asked how he viewed the screen, he said he tipped it all the way forward. Then the other shoe dropped. I checked on my 2017 iMc 5k and, sure enough, the stand nearly blocked the exhaust in that full-down position.
Not believing that could be an issue I rigged a thermometer prob near the vent and fired up component temp reporting software on my iMac. Within minutes the external probe showed exhaust air temps 12-18°C above normal, and the software showed internal temps rising. Sometimes the impossible isn't!
So do those checks please. The external fan fixed a symptom but I fear the cause is still there ands still potentially harmful.
Allan
