I have recently been playing with outboard boat motors that were run in salt water and broken bolts are even more common than my Triumph motorcycles (which I have since sold).
I would do what Benz Dr. said with the addition of spraying a bit of "Freeze Off" on the just the bolt itself when nice and hot (smoking) - and then carefully trying with the vicegrips, just don't use too much heat like Oxy-Acetelyne or even just acetylene as you may bugger up the housing. If you are quick an ice cube may work but you need to be quick so having the vice grips attached and spraying just the bolt is quicker - just don't force anything - if it wants to come out it will come out easily.
I bought a can of the Freeze Off from the local auto supply store and I swear by the stuff now - results have been amazing
Another thing to try is a backwards drillbit that when you drill into the bolt (after flattening and and drilling a small pilot hole) it is putting backwards pressure on the broken bolt and many times that is enough to get it out. Hard to find these so try your auto supply or somebody like Acklands. Harbor Freight may just tell you they don't exist.
If you do get to the stage of an easy-out, stay away from the spiral ones as I have had no luck with those - they break off in the holes and then its a real pain - the tapered rods with a groove on one side work the best after trying the backwards drill bit and first vicegrip, moderate heat and freeze off.