Hi
it's doubtful that it's anything to do with overheating.
It sounds like either a disc or memory problem
but could also be a corrupt driver, or even a missing sound file (if the sounds windows plays for startup or shutdown are corrupt or missing the system can freeze - in control panel stop sounds to prove this) - although you'd expect it to freeze every time.
but let's do the simple things first
... you need about 20% free disc space for windows just to start up and shut down (lots of temp files) ... if the disc is too full ... windows can't create the temp files needed to delete the other temp files (pretty zen!)
so have a look at that
then download cc cleaner
http://www.ccleaner.com/download (it's free)
Use it and clean up any rubbish that's lurking on the disc (if you've been switching off ... there will be tons
use it once a week to keep things tidy (don't select all the options ... just the temp files) ... that way you'll be safe enough.
if that doesn't free enough space .... it's time to ask santa for a second hard disc (fixed or USB) or for a pile of CDs or DVDs to backup all the music, films or whatever it is taking up all the space