You actually just described 2 completely separate problems that have 2 separate causes.... so I guess I'll start with the shutting off on its own...
All laptops have a thermal circuit breaker that's about the size of a finger nail just under the processor, attached to the motherboard. Some also have a secondary breaker under the video card. They're designed to kill the power to the computer if it ever gets over it's tolerance temperature (to prevent the computer from melting). Computers are designed to be able to process data at 100%, process graphics at 100% and have some blockage of the fan without the temperature breaking the tolerance limit and tripping the circuit breaker, but if you have a pet or a dusty house, the heat sink can get so clogged with $hit that the fan just wont be able to keep it cool and it will die.
Usually a user will be doing something graphics intensive when they experience this for the first time (playing a game, watching porn, or watching a DVD are the 3 most common things people are typically doing during their first thermal trip).
So you were watching a movie of some kind... no surprise. Processing graphics is really intensive on the GPU (video card) so the secondary thermal breaker is probably what killed it. The way to fix it is to get a can of compressed air and blow it in towards the fan exit (where air normally blows out of) and blow the air back in towards the grill (push all the pet hair and dust off the grill and in to the fan assembly). Then blow the air up through the fan and out through the grill. Then back through the grill and back towards the fan, and keep switching back and forth till all the giant chunks of hair and crap stop blowing out of the machine.
That will solve problem #1. Problem number 2 is the fact that the machine is freezing. If it's just going really really really slow, then that's strictly a software problem. But if it's "frozen" meaning you can't do ANYTHING, then that means you have a bad hard drive. Essentially when your computer needs to run a process in order to move forward and calls a file from the hard drive and the hard drive doesn't respond with the file, the computer wont know what to do so it will just hang there indefinitely waiting for the file that it's just called. It doesn't know that the file will never come. So your second issue sounds like it's either a massive software corruption, OR the hard drive is failing. Hard drives are designed to last for 3000 hours before they fail, but sometimes, if they run hot a lot, it can accelerate their failure rate... which might have happened when you take the overheating in to consideration.
SO... here's what I'd do.
1) Get a can of compressed air. Clean that baby out.
2) Recover the computer back to factory condition. Press F8 at startup if you need to get in to the machine before hand using safe mode in order to save your docs and stuff to a pen drive. But then you'll need to recover the machine back to factory condition. To return it to the factory-state on Acers, you press ALT+F10 at startup until you enter the recovery console. Also, more and more computers are using F8 and then the "Repair My Computer" option for recoveries.
After you recover your computer, if it's still freezing and acting crazy (or if it doesn't even let you recover it), then it means the hard drive is failing and the recovery partition is on a section of the hard disk that's failed. You'll then have to order a new 2.5" SATA hard drive from amazon.com ( this is the kind you need: http://www.amazon.com/Western-Digital-Scorpio-Cache-Notebook/dp/B0037NYQ6Q/ref=pd_rhf_gw_shvl2 ) and order a recovery DVD from Acer. The DVD's cost about 12 dollars, plus shipping. When you get your new hard drive and DVD, replace the hard drive (they go in on the bottom of the laptop) and then power up the computer with the DVD in the CD tray. Press "next, next, next, next, next, next) and wait forever as it loads the original factory image on to the machine....
And you're done. Sorry for the long post but this issue was complicated. =/
Good luck!