Get left handed drill bits (assuming rt. hand threaded bolt)   heat-cool then try the left handed drill bits.

If you have a wire feed welder its easier welding on a nut and or washer, especially upside down.

Drilling out red hot metal upside down could be real painful. 

Easy outs work IF you get a good set of easy outs, which does not include those cheap arse square tapered easyouts. Throw those things far as possible or leave them on the store shelf.

These are a lot better,

Drill the correct size hole for the shank, then pound the shank in the "nut" is also fluted slips over the fluted shank.

Here is the complete set, which includes guides for the drill bits to keep the drill centered in the hole.

Here is the complete kit and ordering info,,
http://buy1.snapon.com/catalog/item.asp?item_ID=158&group_ID=1254

This isn't harbor freight so yah they are more expensive, I've ordered from Snap-on and they are pretty quick with delivery. 

Here is the left hand cobalt section,,,
http://buy1.snapon.com/catalog/tools.asp?tool=all&Group_ID=19847&store=snapon-store

You can probably find the left hand drill bits cheaper somewhere other than snap-on. ('here' left hand drillbits are totally unheard of,, nobody carry's them!)

No, I don't work for nor represent snap-on in any way.  First time I used the neighbor's easyout set,, I poopoo'ed that gizmo setup,, after removing some broken studs with that kit, I no longer poopoo'ed that easyout kit anymore.

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