Is it normal for a battery charger to become very hot?
The answer is, yes. The charger becomes hottest during what we call the "bulk charging phase", which is when most of the battery's capacity becomes recharged. This is typically 1 - 2 hours after you begin charging, and also 1 - 2 hours before it becomes fully charged.
If the battery is still quite full, the charger will turn green pretty fast, so it won't get into the bulk charging phase which is when it gets the hottest. That's why you won't find it very hot unless it's been charging for at least 1 - 2 hours.
Towards the end of the charge cycle, the charger also goes in the a "trickle-charge" mode, which is when the current gets reduced considerably, just to top up whatever empty capacity is still left available in the battery. This results in the charger becoming only slightly warm, and may last for 1 - 2 hours before the charger light actually turns green.
So if you touch the charger and find that is is very hot to the touch, don't panic. The charger is safe so long as it is below 60 degree Celsius. The best way to measure this is to use an infra-red thermometer, which can be easily bought online for less than $20.
Or if you can hold the charger continuously without scalding your hand, the charger is OK. The best way to describe this is like jumping into a hot spa; while the heat may shock you initially, you will feel fine in a few seconds when your body starts adjusting to the temperature.
So as long as your battery charger is not scalding your hand like a cup of hot coffee, then your charger is actually working fine and doing it's job properly.