Long story short: How is the fan doing in the new 13" air? Does it spin up quickly and how bad is the noise?
The fan did kick in during that lengthy build, it went all the way to max speed and it was loud (+8000rpm). That's totally normal to be honest, my 15" rMBP does exactly the same (and all notebooks I've ever tried, Apple and non-Apple) and it is just as loud
to my ears. Sure, the 15" does finish the build faster so you'll have to deal with the fan noise a bit longer on the Air.
That being said, once it was done with the heavy processing, it rapidly went silent and cool (ah and yes, it did of course get uncomfortably hot during the build but not as unbearable as the 15"... again, nothing surprising considering it had to run on a +150%-170% CPU usage for +20 mins). Under "normal use" (browsing, coding, testing, playing video/audio, etc.), the fan almost never kicks in and even if it does, it's at a low rpm which I consider totally acceptable and find it barely audible under normal conditions (if you're used to working in a completely silent environment, then you'll very likely notice it more easily... that's not my case, the office is a lively place and also at home, I tend to always have something going on around me/in the background... listening to music, some talk show, talking, etc.).
It really comes down to what you are using it for and how often are you pushing its limits (if you do find yourself pushing it almost all the time then it's perhaps not the right notebook for your needs... or maybe notebooks in general aren't the right pick or you just need to adjust your expectations to today's technological limitations). I don't need to build constantly, nor to render/process stuff constantly, so 90% of the time the machine is silent and at most a little warm but not hot to the touch. Yes, every now and then I need to make it lift more and then it might get more noisy and hot... but i'd argue that the experience would be very similar on a beefier machine too (it has been and still is like that on my 15" rMBP and on my previous notebooks as well and also on the latest 15" rMBPs of my colleagues... if you push them, they get hot and they get loud). The main difference between a beefier notebook and the rMBA would be that you'd need to listen to the noise for fewer minutes because things would get done faster... temps might also be better, but the notebook might be also less portable.
For my needs, it has so far been great. It is powerful enough and silent the vast majority of times. The screen is good (I did not spend time putting other machines side-by-side it and compare pixels and nits and screws and bolts however... I just use it, like any normal person would and it's totally fine and more than bright enough - I tend to use it at 50-60% brightness usually) and I'm also happy with the keyboard, it's my first time using a butterfly keyboard actually (I've used tons and tons of keyboards throughout my life and I've most likely already typed way more text than an average person will in their lifetime... I see many people running around and complaining about it, maybe I just got lucky, but I don't feel I needed any adjusting... the only thing I had to adjust to was the slightly bit different keyboard layout than what I was used to - placement and size of the keys).
The best advice I can give you and others is: if you can get your hands on one for a few days, then do so and try putting it to the test. By "putting it to the test", i mean "use it as you normally would + a bit of extra on top". Don't go ahead and run a crapload of benchmarks and all kind of CPU / GPU intensive tasks and processes just for the sake of proving it's not a super-computer... no, it's definitely not, but it might still be a great pick if you give it a fair chance and test it using realistic scenarios (putting it through the phases you would actually/normally put it through).
I get how the price of the rMBA and its placement in the current range of Apple notebooks can be an issue. Is it really worth the price tag? That's totally subjective... Can one find comparable alternatives and ones with even better specs for the same price (or cheaper)? Definitely! I for one like the OS and have been using it for over 8 years now (I've been mainly a Windows user for +20 years... I still use Windows or Linux, or whatever the job might require, but I do prefer the OSX experience) and I really like the build quality, I totally love Apple's trackpads/touchpads and the performance the machine offers is good enough for
my needs.
Sorry for the wall of text, but I do hope you'll find some of the info useful.

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Whenever i start parallels or do something a little intensive the fans kick in and make quite noise.
If you plan on using the Air for similar tasks, then chances are you'll have a very similar experience (at best). Then again, considering that the CPU in the Air could theoretically run without the need of a fan, you could just manually fix the fan speeds at a very low rpm and never allow it to spin up. Should you really do that? Is it a great idea? Well... I'd much rather have the fans spinning up than risk frying things or have to deal with nasty throttling.
If possible, you should get it for a few days and decide for yourself whether it fits your needs or not. If you're already kinda pushing your 2018 15" and you're not really happy with it, then the new Air might very likely be a quite big disappointment compared to your current setup.