One Deck Dungeon Paladin Heroic Feat
The Paladin's ability triggers when you open (flip) a door card and reveal a monster or peril worth at least 4 XP. 

The "with" in the description applies to the door card, not to your character, so having 4 XP in your possession won't trigger anything. 

The description also doesn't mention taking the card as loot as it triggers when the door is first opened or flipped to reveal the contents. You do not have to stay and encounter the monster/peril and can choose to flee after gaining the Heroic die. Note that if you return later, the ability will not trigger again as the door is already open.