[xmpirate]

Nothing really. I did reset the SMC couple of times and also check the Activity Monitor every time the fan speed increases, but to no avail.

[gnyman]

Did you try running the hardware test? https://support.apple.com/en-us/HT201257

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.

[Domenic_S]

Could be dirty. Google a cleaning guide for your model, the fans get all sorts of dusty and it causes thermal issues.

[xmpirate]

Looks like I need to replace the battery as it's near it's end of life - https://support.apple.com/en-in/HT201585