Now that you describe it, I remember having a similar problem with one of my cars - it would start cold every time, but if it got too warmed up it wouldn't start, and this after we replaced the starter once or twice. I don't think we ever did figure out what the problem was - I think we lost the transmission or something and it wasn't really worth getting it fixed.

Mechanics weren't much help, because they would always test the car cold, and it would always work.