I doubt this lockup is heat related. When PCs sit idle, they tend not to generate as much heat as when the processor is actively working, the hard drive is spinning and the CD-ROM is reading data from the disk.
I had a simular problem myself. Let me start by saying I leave my PC on 24 - 7. A few years back, I had a PC running Windows'98 and it was running fine. Then something happened. Every morning when I first sat down at my machine, I would stare at the "Blue Screen of Death" (slang for a hard crash that requires a restart to put things right). Well, as it turned out, the Windows Screen Saver was causing the problem. After I disabled the Screen Saver and just set the monitor to sleep after an hour of inactivity, the problem went away and never returned.
OK enough about my problems. The point is that since your problems start after you stop working, you might try disabling non essential applications and functions, the Screen Saver, etc, and see if the problem corrects itself. If it does, then turn the applications and functions back on, one at a time. When the problem comes back, you now know the cause.
Start using Windows Update, a feature added to Windows 98 and later versions that offers patches, fixes, and other software Microsoft thinks you need to have. Download a small piece of software and your computer will regularly check for new software to download.
If you don't know what I am talking about, and your computer is connected to the Internet, scroll--right now--over to the Start menu, open it, and look for the Windows Update menu somewhere near the top. (If it's not there, do a search for it.) Open the item, which will appear in Internet Explorer, and follow the directions on your screen. when you're through updating your PC, you'll have the latest security updates, patches, and new releases of Windows and Internet Explorer features.