I have the 1.6ghz not for very long I must say, I use Aperture amongst other applications, have watched you tube and apple trailers have and never experienced core shutdown.
One needs to practice some common sense, if you block the air vents yes it will get hot! will it shut down when it gets to hot yes! thats what its designed to do, I have watched HD content and it plays just fine using vlc or quicktime.
In all honesty I don't know what people expect from this machine it does everything I could ever want and about 95% of what most other people would need at home and in most cases work to would need.
Played warcraft 3 over the weekend, max'd out all the settings and it played without a glitch, did it get hot yes, did it shut down no, all the vents were clear the fan spun up to 5100rpm and no problems.
Used it in bed and blocked the vents you can still brows the net, send email and use word. and it won't get hot will run at 50 degrees C
If you want to edit full feature lenght Hd video using pro apps. Its not going to hapen, Thats why Apple make pro products.
Just enjoy your machines, stop looking for faults. I compared mine to my MacBookpro 2.2ghz with 4gb ram and a 320gb hard drive and in all honesty could probably sell it, this little air could do everything I threw at it!
Hope this helps.
Happy MacBook Air owner.