The Thorium Brotherhood is a faction from the original WoW game, and it used to be really tedious and expensive to get. Some people on Wowhead used to suggest that this rep should have been part of the Insane in the Membrane grind.

Except now it is both easy and worthwhile to take a little bit to get this reputation to at least Revered.

A lot of people in the blogosphere have discussed this, but the reason you want Thorium Brotherhood reputation is simple: +22 Intellect to weapon. Back when heirloom weapons were first introduced, the ideal enchants for the caster weapons were Spellpower or Healing Power. But with class mechanics changes from patch 4.0 forward, the +22 Int enchant is now the Best in Slot enchant for caster heirlooms. (Or casters in the 19 or 29 twink bracket.)

So, how do you get this reputation? There are two methods, and I'll discuss them both, as well as how to get the formula once you have the needed rep!

The cheap, time-consuming method
Recommended for: Future Loremasters, enchanters doing this grind at level (47-58), anyone with less capital than time

Because I love my nerd points, I used this method to get my Thorium Brotherhood rep.

This method is fairly simple:
1. Complete, in full, the quests in the Searing Gorge. This is, I believe, a level 47-53 zone or something like that. You can reach Searing Gorge on foot from Loch Modan or the Badlands. You no longer need a key to unlock the gate from Loch Modan to Searing Gorge; you can, in fact, simply walk in.

Don't directly go to Thorium Point. Like in all Cata zones, the quests chain, so you need to do a lot of seemingly unrelated quests. However, once you've finished the zone, you should be somewhere in mid-to-high Honored reputation, depending on your race and guild level. However, you need Revered reputation for the enchanting formula!

2. Luckily, once you've completed Searing Gorge, you'll unlock Master Smith Burninate, who will accept Dark Iron Residue turn-ins. This item drops off Dark Iron dwarves found in Searing Gorge, Burning Steppes, and Blackrock Depths. It doesn't bind, so you can also farm it up on a higher level toon, or buy it on the AH.

The faster, slightly more expensive method
Recommended for: People who aren't planning to quest Searing Gorge and want that formula now!

Luckily, for those of you who don't like questing, there's another method! You can turn in items to Lokhtos Darkbargainer in the Grim Guzzler inside Blackrock Depths for reputation. He's conveniently also the guy who will sell you the enchanting formula you want.

You'll want to buy either Fiery Core or Lava Core. These should be fairly cheap, since everyone and their mom is soloing Molten Core for the legendary weapons now. Wowhead tells me that they give about 2000 rep per turn-in up to Revered, although my guild leader who just did the turn-ins reported 550 rep per turn-in. (That may have been when he was working on Revered to Exalted, though.)

Getting to Lokhtos Darkbargainer

No matter which method you use, you'll eventually have to get into the Grim Guzzler in Blackrock Depths to get the formula. While you can now get in there fairly simply, it's pretty easy to get lost in BRD.

But there's another way: Anyone with a Direbrew Remote from Brewfest can port their party directly to the Grim Guzzler. This is especially useful if you're planning to learn this formula on a lower level toon. Definitely see if you can get a guildie to take you there if you don't have a remote on the toon learning the formula. Since my enchanter is also my blacksmith, I got a ride there by offering my blacksmith's services in making the Sulfuron Hammer to my guild leader. (The pattern for that is also obtained from Mr. Darkbargainer.)

If you have to hoof it, here is a video showing how to get there. It's slightly older, but I believe the path is still good.

Enjoy your shiny new heirloom enchant!