The car is my 88 Accord LX-i, and the problem has lingered for years. I'll describe the behavior. Suppose I start the car when it's cold and drive it a short distance, usually less than a mile in the town in which I live, and park and turn off the engine. At this point, the temperature gauge is usually showing some warm-up, perhaps not quite to normal operating temperature yet and the distance driven was not long enough for the engine to be thoroughly warmed up. I'll go into the post office or bank or wherever for a few minutes, I'll come back out and try to start the engine and it won't start. It cranks fine but won't fire. I discovered long ago that waiting a few minutes and then trying again will usually result in a successful start. But, continuing to try to start right after first trying is futile; the car simply will not start until I've waited a few minutes.
Again, cold starting is never a problem. Likewise, the problem does not occur if I've driven long enough for the engine to be thoroughly warmed up before shutting down. However, hot starting is not consistently smooth; sometimes, the engine (hot) runs rough for the first few seconds after starting.
Within the last few months, the following parts have been replaced: coil, distributor (a new Richporter), spark plug wires, and spark plugs. One fuel injector was also replaced to resolve a leaking injector problem.