I agree with Chris Green -- it sounds like a shutdown caused by overheating. You can try running the free [http://bresink.de/osx/TemperatureMonitor.html|Temperature Monitor] to verify that. I don't know how many temperature sensors that model of iBook has -- probably not too many -- so you might not get a fix on just which component is overheating, but you should at least be able to see a main temperature and see it keep rising up to the shutdown point.
If you do confirm that it's overheating, you might open the iBook back up again a) to see if anything got dislodged or disconnected when you replaced the hard drive, b) to check for dust buildup or a malfunctioning fan, and c) (if you feel up to it) to reapply the thermal grease and reset the heatsinks as Chris suggested.
You can also check to see if you have the same problem running on the battery as you do running on AC. If it doesn't heat up when running on the battery but does on AC, then the charging system may be malfunctioning and heating things up.