Hearthpwn

Overview:
Control the board with taunts and hold him off until fatigue.

Mulligan:
Mulligan for Barnes and Silence.

Early Game:
Silence the Rod of the Sun, before you kill it, preferably on turn 1. Otherwise, it will go into the resurrection pool. If it does, it's not the end of the world, but it will make more work for you. Remove as best you can and heal, until you can drop Barnes on turn 4.

Mid Game:
Now that you likely have a taunt or Catrina Muerte out (Convincing Infiltrator or Obsidian Statue is preferred, but having Catrina Muerte rez herself each turn isn't too shabby), the game get much easier. Continue controlling the board, rezzing, and healing if need be.

Late Game:
He will be close to fatigue now, so all that you have to do is answer his few remaining threats and continue hitting face.

My Other The League of Explorers Decks:
Temple of Orsis
     Zinaar (Mill Mage)
     Sun Raider Phaerix (Resurrect Priest)
     Temple Escape

Uldaman
     Chieftain Scarvash
     Mine Cart Rush
     Archaedas

The Ruined City
     Lord Slitherspear
     Giantfin
     Lady Naz'jar

Hall of Explorers
     Skelesaurus Hex
     The Steel Sentinel
     Arch-Thief Rafaam
     Rafaam Unleashed