I beat Heigan with an early version of this deck, then refined it and beat him again. He should be a piece of cake with this cheap deck!

Strategy

Basically almost every minion in this deck survives or benefits from his hero power. Egg gives you the minions and golems and creepers eat hero powers for two turns, allowing you to spam out even more cheap minions and gain control of the board. The beginning is the trickiest part but once you control the board, you've won.

Mulligan

You want to make sure you have Sacrificial Pact or Corruption on your starting hand - it doesn't hurt to have 2 of them either. That way you can deal with his early board minion. If its deathrattle spawns something ridiculous like a Doomguard, it might be a good idea to just concede and hope for a voidwalker next time. Nerubian Egg is also a good starting card.

Extra information

It's usually not a good idea to instantly remove Heigan's first minion on the board - he really likes to buff them up with Demonfire so you can get some nice 2-for-1-value if you wait with killing it off until he's buffed it.

Remember to be clever about your positioning. You want to put anything with a deathrattle or divine shield or high hp to the left, and cards like Flame Imp and Doomguard to the right.

I've seen some people run Gurubashi Berserker which seems like a very strong card in this matchup. If you want him in, you can swap out the Mogu'shan Warden.

Good luck!