I realize 2 amp isn't the mains current. The difference is that the 13 amp plug wasn't designed to have any active components in it, just the connections and the appropriately rated fuse, so nothing that should generate significant heat.
Putting the AC->DC and voltage conversion circuitry in the plug is another matter. As has been commented on elsewhere, even separate brick battery chargers often get significantly warm.
Putting the AC->DC and voltage conversion circuitry in the plug is another matter. As has been commented on elsewhere, even separate brick battery chargers often get significantly warm.