Q: fan starts working almost immediately

Apple has a 90 guarantee on repairs made outside the warranty period.

Check your Activity Monitor when that happens:

https://support.apple.com/en-us/HT203184

You might also run an Apple hardware test:

https://support.apple.com/en-us/HT201257

Note that an error free AHT is not definitive.

Ciao.

Resetting the System Management Controller

Apps affecting mac performance, battery,temperarure and fan activity.

https://support.apple.com/en-ca/HT203184

Would it be possible to download and run Etrecheck, then post the list here.

http://www.etresoft.com/etrecheck

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