Acer ........?

All laptops (especially the older ones) will heat up when running, regardless of batteries or not which is why people sell laptop cooling solution (e.g. fans). I had an acer, I thought the heat generated is quite alright compared to other brands. You might want to get the service centre to make sure your internal fan is working.

I think it's because they use a battery with incorrect and not maintained.

I do not think so. I have a acer and I work for hours with battery on and nothing happens. May be my acer is new. when it ages, it might develop such problem as you mention.

Do not you never use the battery at all. At least every week, take your laptop to work with the battery so that the cells inside to keep working regularly.