Q: macbook air fan is suddenly very loud

Try a SMC reset:

https://support.apple.com/en-us/HT201295

Check Activity Monitor, ALL PROCESSES:

https://support.apple.com/en-us/HT203184

Run an Apple Hardware test:

https://support.apple.com/en-us/HT201257

Note that an error free AHT is not definitive.

Ciao.

Apps can affect Mac performance, battery runtime, temperature, and fan activity - Apple Support

Linc Davis wrote:

 

Apps can affect Mac performance, battery runtime, temperature, and fan activity - Apple Support

Since I have already provided a link to this Apple support article, your post is redundant.  But I do thank you for your apparent agreement. 

Ciao.

Ogelthorpe, I don't see the post that Linc Davis added as redundant in the least bit. I see it as his merely adding some advice on what could possibly be additionally affecting dmrosen's original issue. I've spent over 20 years in the Apple realm - as an Apple support specialist and as an Apple employee and never once did I lack modesty or humbleness when it came to Apple support or advice. You sir, should re-read your posts prior to saving them on the forums. To say you come off as rude is also quite redundant.

I can only speculate that you did not click on the links that I included in my original post.  The second one was this:

https://support.apple.com/en-us/HT203184

Should you click on the one that Linc Davis posted, you will find that it displays the SAME (redundant) Apple support article as the one I posted.

In light of the facts, I have no reason to modify or retract any thing that I have posted in this discussion.

Should you still feel differently, please let me know.

Ciao.