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I have an extra 7200 RPM hard drive I could put in my late 2013 21.5" iMac EMC 2638. Just want to know if it would run hot. It’s WD black drive. The iMac is already apart and has been for a long time.

Your system is limited to a 2.5" SATA drive. Here’s the IFIXIT guide: iMac Intel 21.5" EMC 2638 Hard Drive Replacement. As for running hot, you’ll need to check the given drives specs to see if its within the same range as the Apple HD.