I ran into this problem with a Dell Latitude D830 laptop with a Lithium Ion battery. Here is what happened and how I resolved it.
The laptop is several years old with the original battery. I normally keep it unplugged from wall power when not in use (no power brick nor docking station). My typical use is checking e-mail each morning with some light programming. I will normally just close the lid after use, causing the laptop to go into sleep mode and unplug it so that it maintains state on battery then plug it back in before opening the lid to resume.
Events leading up to the hot battery during charging
Recently I thought I had shut the laptop down and put it away for a week however what appears to have happened was it was instead in sleep mode on battery until the battery exhausted.
When I started the laptop up, plugged into the wall with an adapter, while on a trip, I saw the Windows not shutdown correctly message and realized what I had done. I saw the battery begin to charge.
After about 45 minutes of use, I realized that there was a red charging indicator in the Windows 7 taskbar as well as a red charging indicator displayed on the laptop state icons built into an area beneath the screen. Then I realized that the edge of the keyboard area above where the battery is inserted was uncomfortably warm. I shut down the laptop and removed the battery pack which was abnormally warm, almost hot.
The red charging icon in the Windows 7 taskbar showed a mouse over message of the battery being some percentage charged but that it was no longer charging. I think it was around 95% charged at that point.
I let the battery cool down, re-inserted it into the laptop, started up the laptop to continue. The green charging indicator showed followed shortly by the red charging indicator. The battery was once again uncomfortably warm.
I shutdown the laptop, removed the battery to let it cool, and continued my work using the power adapter with the battery removed.
Procedure that appears to have corrected the issue
What I did to correct the problem was with the laptop turned off and disconnected from the power adapter, I re-inserted the battery and turned on the laptop. I then did some reading on various news web sites while keeping an eye on the battery charge. After a bit the battery charge dropped from around 90% to around 30%. During this time the battery temperature seemed quite normal.
I then shutdown the laptop, reconnected the power adapter, and saw the green charging indicator in the laptop state indicators beneath the screen. I turned on the laptop and started up Windows. I then let it sit for a few minutes monitoring the battery indicator in the Windows 7 taskbar and checking the battery temperature with my hand. The battery temperature appeared normal, slightly warm from charging, and the charging indicators in the Windows 7 taskbar and the laptop state indicators both showed green indicating charging normally.
I let the battery continue to charge up to 100% at which point the charging indicators in both the Windows 7 taskbar and the laptop state indicators turned off.
Since doing this I have not seen the problem with the hot battery and red charging indicators.
What I think happened is that the laptop battery was almost totally discharged during the week it was in sleep mode with no alternative power source other than the battery. The battery was discharged more than would normally be allowed because the laptop was in sleep mode.
When I started the laptop up with the almost totally discharged battery, the charging circuitry and software did not properly handle the battery charging process resulting in the battery becoming overheated. When the battery became overheated, it stopped charging however the charging circuitry and software continued to try charging the battery.
When I used the laptop on battery only, the battery charging circuity and software was reset or recalibrated and the battery charge level was such that once the laptop was reconnected to line power the battery charging was within normal parameters and the charging circuitry and software performed correctly.
I have not seen this abnormal charging behavior with the hot battery over the last few days. The Windows 7 taskbar charging indicator shows battery at 100%. Disconnecting line power I see that the charging indicator immediately shows 98% and then shows a slow but steady drop as I surf the web. My impression is that the battery is good for about 30 minutes or so which is about what it has been before the abnormal charging behavior. Over the course of several years the battery capacity at full charge has slowly dropped from the original 2 hours or so.
I am of the impression that my laptop battery was not damaged to any great extent by the abnormal charging with battery becoming uncomfortably warm. As far as I can tell the battery capacity was not affected as it has been steadily dropping over the course of years from age anyway.
Another Dell laptop purchased at the same time used by a different person at home spending most of its time in a docking station has a useless battery. It can not be used on battery for more than about 5 minutes so it seems to me that removing line power when not in use is a good procedure to follow.