Light heat with a propane torch is OK.
Obviously, watch for an oil fire.
You could also try some PB Blaster spray to loosen it
(but don't apply while you have an open flame nearby!)
My preference for removing these (and I've removed many broken studs), is to use a left-handed drill bit.
Center punch the broken stud with a good center mark and drill into it with the LH drill. Since the electric hand drill will need to be turning backwards, it will tend to try to twist the broken piece out. Often, when you're about 1/2 way down into the stud, all the twisting and vibration will cause the stud to unscrew.
And for the record, I dislike Eze-Outs. They tend to "wedge" the stud tighter and then break off, leaving a hard, un-drillable piece of steel in place.