In X-Men Origins: Wolverine (2009), Wolverine is able to decapitate Deadpool, who if I understand correctly, had a bone structure made of adamantium.
But later in The Wolverine (2013), which, correct me if I'm wrong, but I assume it's part of the same continuity, Wolverine fights Silver Samurai, who pilots a robot made of adamantium. When Silver Samurai attacks him with his adamantium sword, he's able to hold him back, but as soon as Silver Samurai turns one of his sword in a burning sword, Silver Samurai is able to cut through Wolverine's adamantium claws with his adamantium burning sword.
Later, when Wolverine has the chance to attack Silver Samurai again, instead of attacking him with his other intact adamantium claws, he looks for one of the Silver Samurai sword that this last dropped, and in desperation screams "come on!", expecting the sword to start burning, like if that was the only chance he had to harm Silver Samurai. Then, with the burning adamantium sword, he is able to cut the robot head made of adamantium.
Why didn't he use his adamantium claws to cut/harm Silver Samurai? Can cold adamantium cut through adamantium?