MacBook Air starts heating up on the left side of the keyboard?

"Lets try this - Shutdown your laptop completely (so its at room temp). Restart it and don't load or access any apps (disable any that preload). Take a measure with Temperature Gauge is the fan still at full tilt? If it is and stays running lets do a reset. Follow this Apple TN: EFI & SMC firmware updates for Intel-based Macs. Test again did it resolve the problem? If not did you get your system wet as some point? You will need to open the case to inspect things and will likely need to do a cleaning of the dust buildup on the logic board & fan. Let us know what you see first.

Next Test:

Let the system run without any alterations (at rest) with Temperature Gauge window visible so you can see it. Do you see the system starting to get too hot (Temperature Gauge will change the bars to yellow and then red). If you do you know something is running in background. You'll need to load up Activity Monitor to see what process is chewing up the cycles. Sort out the list using % CPU column so the heaviest is on top. Take a screenshot again and post it here.

Next Test:

If that didn't show any problems run your web browser (only) access what you normally do with Temperature Gauge window on the side so you can see it as you're running what action do you see the system starts to get too hot (Temperature Gauge will change the bars to yellow and then red). Then you have something running in your browser that needs fixing (like Adobe Flash) go though what you have added and make sure they are all up to date. Flash does push the system so it would not surprise me if that ramped it up but it should not be getting as high as your system had gotten.

Some new Q's:

What is your storage HD or SSD?

How full is it?"

"You need to get a good temp & fan monitoring app. Checkout this App Temperature Gauge Pro. There are others but this one is the one I like the most.

See what it tells you and post the output here for us to see."

"There are several cause of heat buildup:

Clogged heat sink, blocking heat dissipation, or

Stuck process, very high CPU usage, running the system hot, or

Intense but normal use.

For the first scenario, put your laptop in a well ventilated place, if it doesn't work, clean the heat sink.

For the second scenario, try to locate and kill the stuck process, find the cause for the software issue, update the software or avoid triggering the bug again

For the third scenario, some applications are known to be intense, flash player to be an example. Take a break, have a cup of tea."