a battery on power will charge every time she drain a bit sometimes that cause the battery to overheath
Constant charging can ultimately kill battery life. This is the reason why some laptops will only charge the battery up to 80% unless you override the power options to do a 100% charge up.
Whether or not that will actually prevent "battery kill" is unknown to me. If the battery is going to be plugged in most of the time then I would simply remove the battery once it is 100% charged. That is what I currently do. If I know I will need to bring my laptop with me then I simply install the battery to bring the charge back up to 100% since batteries discharge themselves slowly over time.
Every battery have a protection circuit.So It can't be charged when full.Don't worry.
If you could overcharge a Li-ion battery like those found in most laptops, it would rupture(safety valve to let out pressure to prevent explosions). So the charger HAS to be smart and stop.
You have nothing to worry about.
The 80%(or 30-50%) idea is supposed to allow the battery to last longer in cases when you leave it plugged in all year around. They say leaving it full charge is bad for its overall health, but I have had no problems with it.