MacBook Gets very hot at plug, When charging & when in use..,

If your adapter "brick" is resting on a soft surface like upholstery, bedclothes or a carpet, it will heat up more than normally because air can't circulate freely around it. Rest it on a hard flat surface, just like the MBP itself.

The charger will also get hotter when the machine is in use than when it isn't, all other things being equal, because more power is being drawn from the adapter to power whatever you're doing. When charging the battery is all that's happening, the adapter doesn't need to supply nearly as much power, and runs considerably cooler.

It's also true that the charging process itself draws more power and generates more heat early in a charge, i.e. when the battery is deeply drained, than it does later, when the battery is closer to fully charged. The charging current tapers off sharply as full charge approaches.

If none of these little explanations seems to address the circumstances at hand or the behavior you've observed, you can always take your machine and adapter to a Genius Bar and have them tested without charge. Just make an appointment first:

Genius Bar Reservation and Apple Support Options - Apple