You should replace the plug, and when you do cut back the cable past any section showing signs of overheating.
Even if the socket doesn't look damaged, overheating may have damaged the temper of the spring contacts for the plug pins, and so you could get the same problem even if the origin of the overheating lay in the plug, so you should replace that too. Again, inspect the cables where they go into the terminals, if they've overheated (darkened or hard insulation) cut them back, as the copper will have hardened,and the screws in the new socket won't bear down on the conductors properly, so poor contact, and more overheating.
Obv power off (a good way to check if you don't have a proper tester is to plug a light of some sort in, and do an off-on-off-again cycle of the breaker, which will prove you got the right breaker and that the light didn't coincidentally fail just as you switched it).
Bear in mind that if you have an RCD, even with the breaker off, if you touch N to E the RCD will trip, so warn people in the house, don't do it when it's dark, or when someone is using an electric shower, or she-who-scowls-at-you is drying her hair or watching a favourite TV show, and maybe shut down any mains-powered computers as a precaution.