Things to do/check before warranty is up

Run the diagnostics on it. By the way, it's not a good idea to leave a power on laptop in a bag. Ventilation can be blocked causing it to overheat.

That fan issue happened all the time to me when I had my Mid-2010 MacBook Pro. It appears to be some sort of driver issue, which I'm pretty sure was fixed with the 10.7.2 update.
Other than that, I would say just take your computer into the genius bar about a week before the warranty is up and have them run a hardware test on it to make sure it passes. At that time also be sure to mention any issue you may be having.
In regards to AppleCare, some people say it's like an issuance plan, where nothing might happen and you just wasted the money you spent on it, personally it's a gamble that has paid off for me 2 times. On my Mid 2009 13" MacBook Pro, the display failed and was replaced for free when it would have been $400. My Mid 2010 MacBook Pro also ended up with a failed GPU, and the logic board was covered (normally $700). I must say though, my laptops go everywhere with me, and although I keep them in good shape, they are constantly being used to run resource-intensive programs which may have an adverse affect on the lifespan of the computer.

bender644 said:

I'd like your thoughts on what kinds of things you would do to check the MBA's sturdiness before the warranty is up. I'd like to make sure it can handle the toughest tasks so I'm not presented with any surprises 8 months from now.

Thanks for your comments.

Bender

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Just check all aspects for proper function. Running a diagnostic will only tell you what is currently NOT working correctly. There is no diagnostic you can run that will predict what may fail in the future.

bender644 said:

A little while ago, I put it to sleep, then in a case and in my bag. When I got home 30 minutes after, I took it out of my bag and the fan was running on full speed. It was pretty hot. Everything's been fine since, and it hasn't done it again. It's really been put to the test.

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Hi,
I think you are fairly lucky...my bro-in-law did the same thing to his older 2007 MacBook Pro, but only he left it in the back for about 2 hours...the whole laptop was slightly warped after that amount of heat in an enclosed area for so long. It actually ran fine since...it died about 4 months ago...it was just under the 5 year mark.

My take...with the SSD, and the speedy boot times, now, I don't really use "sleep" anymore, I just shut the thing down! Believe me, this is quite a change for me, I've been using Powerbooks since 1996 and *never* shut them down, I always used sleep. But, the fact I can be up and running in 20 seconds from a cold boot has changed all that. I find that my Air just uses too much battery juice while sleeping (I have the 2009 model, never got more than 4 hours on a charge).

BTW, I always get the extended warranty on my powerbooks/macbooks. There is too much that can go wrong with these machines, Apple pushes the limits on design and engineering, and picking them up and taking them around. I hate the expense, but I try to re-coup it by selling the thing on ebay at the 2.75 year mark, and usually get a little extra by saying the warranty is good for 90 more days (the warranty *is* transferable).

HTH!