For the last year and half I have been removing broken bolts in a new to me way. At work we have some big blow mold machines that break bolt from time to time. Who hasn't ran into one of those? They are normal on the head area of the machine where the bolts are anywhere from .75 to 1.5 in diameter and its in steel that's 350 to 400 degrees. Always grade 8 Allen caps. Previously we got the hammer and punch out or welded a smaller bolt or nut to the broken bolts. We have found with great success that the best way to remove them is with a air operated tool engraver. Yea the little thing you used to engraver your name on your hand tools. Quick and easy to use even upside down like we normally are. The only issue that you need to watch out for is hitting the thread itself. The electric unit also, work just not as good.