Carl,
I have two Homelite 240 chainsaws. And, they act the same as yours. I have suspected it is the ignition that gets hot and then won't fire. When it happens again I will use some engine starting fulid to make sure it is not the fuel system. My 240s are more than 20 years of age and the ignition systems have never been replaced. I have found that it is usually the condensors that go bad. The points, however, sometimes go bad too. Let me know if you solve the problem. My email is:
tedmeredith@yahoo.com.
Good luck
Ted Meredith, November 2006