MacBook Air Fan Problems
Have you tried using an app called smcFanControl. It's a nifty little program that can directly control the speed of your fan.
You can also check the CPU temperatures to see what's making it hot - if indeed something is. Even when it gets hot it can take a while to cool down again.
It's usually something in the background that causes this.
Open Activity Monitor in Utilities, and click on the CPU tab, so that the programs that are running show up with the heaviest users first. That will show you what's using most resources, and thus causing your fan to run.
Things like iCloud, Dropbox, Photos updates as they synchronise with the cloud services can also cause a lot of activity, thus overheating the system and causing the fan to overrun.