When the battery is at 20% then all bets are off. Yes I think someone could do a better job of explaining why but I'll just nod and write that I would not expect this to work. Let's see if anyone will write a longer explainer.
At 20% it is time to plug it in.
As to the CPU getting hot when it runs at 90 to 100 per cent, that's normal too. I suggest you find out what the machine is doing as when it is on battery power such high usage can drain the battery faster and cause early shutdowns.
HP G60-440US WIN7 Home 3GB RAM
I use MSE for security and Chrome
My Laptop has now shut down when on battery power 2x and then it will not start unless I disconnect & reconnect the battery. I just did this without even plugging it in and the battery still had 20% juice left. In addition, I have noticed it running very hot a few times but that has been, I think, because the CPU is addressing something and operating at 90-100%.
Also, I did a system restore after the first incident 3 days ago and it just happened again.