Like all electrical devices, battery chargers are not 100% efficient. A portion of the electrical energy the charger consumes to create direct current is expended in the form of heat. This heat radiates from the components inside the charger to the surrounding free air.
The highest temperatures for certain components of a randomly chosen charger as actually measured by Underwriters Laboratories are listed below.
Transformer secondary coil
108 C (226 F)
96 C (205 F)
42 C (108 F)
DC cord at strain relief bushing
51 C (124 F)
22 C (72 F)
The two components that people can actually touch are the external case and the DC cord. For most people, the threshold of pain depends mostly on the degree of skin callusing but is typically between 41 C (105 F) and 52 C (125 F).
Note how this compares with the case and DC cord temperatures. For some people, these parts may very well be perceived as "too hot to touch". But is this a cause for concern?
Every single component in a charger must pass very demanding tests before it can be certified as approved by UL or other approval agencies. If the charger is used as intended, the heat perceived as excessive is normal and within its limits. Remember that the temperatures cited were the maximum reached.
A useful, if not an exact laboratory-accurate rule of thumb, is that if you can touch the component in question lightly and count to three, there is no cause for concern.
We suggest that the area of most concern for our customers would be to monitor the critical DC plug connection for excess heat. The contact tips and blades here are subject to wear, particularly if the charger is old and/or used on a daily basis. A poor or loose connection here will create heat beyond design limits, scorched and burnt parts are not that uncommon.
If there is any doubt as to the integrity of this connection, inspect and replace as needed.