I just defeated Emperor Thaurissan on heroic with a special mill druid deck build for this fight.
He draws a lot of cards himself and helps you to get through his deck. You need some luck as always, but if you get lucky he draws lots of cards at the beginning and you can burn lots of cards at the same time. But try to get the Crazed Alchemist as fast as possible out there so the princess doesn´t do that much dmg anymore.
Key cards and why you need them:
Grove Tender if you need mana crystals but most of the time for card draw
Keeper of the Grove as a silence and in rare situations u can kill a minion
Crazed Alchemist to switch the princess so she does not die to the aoe effects
Ironbeak Owl for extra silence on the taunts
Thats it! It took me 3 trys and I switched some cards, but this setting got me the win. Do not worry much about his life, just try to stay alive and kill his minions. Try to burn lots of cards, so you have to deal with less threats. At the end of the game the mill will do the killing for you ;-)