I was thinking if a burn deck is a viable deck.

So here is a try :

Hero :
Tazo (as I will use mostly Fire abilities, Tazo seems to fit)

Quest (14)
3 It's a secret to everybody
4 Into the maw of madness
3 Counterattack
3 Torek's Assault
1 The Princess trapped

Allies (16)
4 Scout Omerrta
4 Grunt Baranka
4 Vesh'ral
4 Waz'Luk

Abilities (25)
4 Fireball
4 Fireblast
4 Scorch
4 Blistering Fire
1 Pyroblast
4 Mana Agate
4 Arcane Missile

Items(5)
1 Trance Stone
2 Netherwind Crown
1 Ancient Cornerstone Grimoire
1 Penelope's Rose

No control, just throw everything at the opponent's hero :D

with 25 abilities id take the
3 Torek's Assault
1 The Princess trapped

or

4 Into the maw of madness

for 4 zapped giants
no frost nova?

Frost Nova is control element, I just want to burn a fast as possible.

Zapped giant, why not

I would be tempted to play the Blood Elf Horde mage from BC, so I could use Solanian's Belongings, but maybe that's too slow.

some things to consider:

Whitemane's Chapeau would let you recycle Abilities.

Also, there's an equip that when it comes into play let's you reveal the top 3 cards and keep all revealed abilities. I can't remember the name of it but that seems like it might be useful.

EDIT: Belt of the Archmage