There's a cool little free program called CD Wave that you can get from
http://www.milosoftware.com/cdwave/
[Well, it's free for 31 days but it doesn't stop working after that. That said, of course you should support the developer and pay for it.]
It will record the stream for you, but you'll have to set your soundcard's source to be (and this may vary slightly depending on your soundcard) Stereo Mix (or soundcard output or whatever).
NOTE: This will record whatever sounds your PC is making. So if the stream is playing, you'll get that. If your PC beeps because you just got an email or anything like that, it will record that too. (I don't mean it will record fan noise or anything like that, you'd have to set the input source to microphone (and have a microphone!) to do that.)
After you've recorded the show, CD-Wave can also cut it into tracks for you to burn to CDs if you so desire, and save them in many formats. However, I don't think it can be set to automatically start recording at a certain time. Perhaps that feature is there and I never noticed it though.
[edit] OK I just checked, that feature is there... "Start Recording At" and you specify a time. Sounds like what you're looking for! [/edit]