I feel the same applies to Macbook as well. I've a Macbook Pro Retina 13 inch, early 2015 at a battery cycle count of 1001. From the last few weeks, the system is terribly slow. I randomly see the fan speed going berserk. :/
iFixit guide for removing your heatsink: https://www.ifixit.com/Guide/MacBook+Pro+13-Inch+Retina+Disp...
My favorite thermal paste: https://noctua.at/en/nt-h1.html
I had a old Air which ran very slowly and fans spinning like crazy due to a issue with the cable from the keyboard/touchpad. Apparently if the SMC does not get proper signals it will go into a "failsafe" where things work but slowly.
Probably not the same issue, but just a little anecdote on a similar symptoms caused by different issues so that nobody gets tunnel vision on the battery, which might very well be the cause in this case.