Hi Susan,
Before extending an educated guess as to the cause of your issue, having a little more information would be helpful.
What type of ignition system are you using (i.e. original points-based system, electronic ignition, CD system, etc.)?
What did your engine rebuild entail (i.e. full rebuild, carburetors, etc.)?
Were there any other changes made (i.e. fuel delivery, exhaust, other, etc.) that was incorporated as part of the work surrounding your rebuild and engine reinstallation?
You mentioned the no-start when hot. What was the temperature gauge registering when the car would not start?
A number of issues could be causing a no-start condition when hot. Since your rebuild could have disturb other supporting components including ignition, fuel delivery, carburetion, wiring, etc., further symptoms and information would help narrow down the cause.
Ray (64BJ8P1)