You should be able to tell if there will be a problem, your charger will get hot not just warm, the same thing with the battery if it feels hot that means there is a short in it and you should not use it. I would just leave it unplugged when not in use to be on the safe side. I've used laptops with bad batterys for years with no problems and the charging liite were always on.As long as the battery dosen't short out it will be fine.
The charger is warm, but not "hot" per-se.
The battery itself is cool, does not feel warm, but that could be because of the casing, it has a shroud covering it.
Warm is pretty well normal for most chargers, how long dose the laptop run doing normal stuff like surfing the net with the charger unplugged ? If you get 2 hours out of it I'd say don't worry about it.