I updated ed to Sierra a quite a few months back. I had no problems, computer ran as before except for needing software updates. Then in Sep 2017, I got an iPad pro and decided it was time to try out the keychain sync over iCloud which I never had used before. I set it up on my iMac, Mac Mini, MBA, iPhone and iPad Pro. For the past couple of weeks I began noticing my MBA was running though battery life about 6 times faster than before and also that the fan was constantly LOUD, even after start up with no open software programs, and underside of the MBA was hot enough to redden my thighs in short order.
Today I was wondering if the overheating was the fan or the battery or both so I started searching and came across people with this problem after the Sierra update. So I tried all the posted solutions from Apple Support and forums.
Finally, the only one that worked, was force quitting the keychain access in Activity Monitor and then disabling Keychain sync in iCloud. It worked like magic. The fan is not audible in the least anymore and the battery life has held over the past hour (-7%) instead of dropping 30-40% an hour. And the underside of my MBA is no longer hot.
It would seem, at least in my case, that activating the keychain sync over iCloud was somehow related to high fan speeds, reduced battery life and my MBA heating up more than usual. By turning off these features, the problem was resolved. At least for me.
I have used a password manager program nearly 20 years so killing off the keychain sync was no biggie for me. It was more a convenience of being able to use Safari autofill across devices. I returned to using my password program set to launch in my preferred browser and using the password manager's app on my devices.
I hope my experience will help others.