To me this sounds like a simple overheating problem, and by the sounds of how you treat your computer, it would by all means make sense. All computers, like people, need their sleep. By that I mean a full shutdown, with nothing running or continuing to quietly operate. Sleep or standby mode, while most of the time a perfectly good state to put your computer in, is not a full time way to go. That's like living through life with naps every now and then, and never having a full 8 hour nights sleep.
You may have noticed after a while of having it only been on sleep mode (a couple of days or weeks maybe) that things start to slow down.. maybe a program takes a little bit longer to open or close. While on, your computer stores things in it's memory (or ram) and even if your computer has plenty of ram (which if my sources are right, your laptop only carries 512mb, which is pretty small for todays computers) eventually the space will be taken up. Constant running like this can wear the insides of your computer down.
The battery can also be a culprit (I would definitely suggest getting a new one) and if it can only last 20 minutes, it has some definite faults. Also, for future reference (something I didn't know for quite a while) your battery needs to be worked every once in a while. Leaving it plugged in constantly will also wear down the battery faster, and some exercise with it unplugged will help a new battery get used to different situations.
Clear up some space on your laptop and run some programs to clear all your temporary files once and a while. Downloading and running TFC
along with giving your comp some FULL rest time, once and a while will surely help speed things up and lessen overheating. Buy a new battery and exercise it sometimes. Like I said, I'm no expert, but as no one has replied yet, I thought I'd suggest some things. More advanced techs can probably tell you more, but until then..