MacBook Pro Hardware – High Fan Speed and CPU Temp with Low CPU Usage

There are two likely issues afoot here:

1. Your System Management Controller has gotten some corruption.
2. You're seeing potential hardware-/sensor failures.

To reset your SMC, follow these instructions: http://support.apple.com/kb/HT3964

If that doesn't solve the problem, I'd run Apple Diagnostics and see whether it picks up on any hardware problems. If it does, the system should be taken to Apple or an Apple-authorized repair centre for further testing and repair.

Go to iFixit and look up the guide for your Air. You will need to do two things. First is disconnect the battery, second is remove/clean the CPU heatsink before reapplying thermal paste and refitting it. When you've done that you can reconnect the battery and see what happens.

SMC resets using key combos don't always work - disconnecting the battery does. It might seem drastic but removing the power source is what's needed. If you've an SMC issue (which sounds very likely) this should clear it and cleaning up the CPU cooler will give you something useful to do while any residual voltage is discharging.