intermittent problem - car starter dead, no start

[mlipmd]

Twice now I have gotten stuck with a no start situation. The car has always started instantaneously on turning the key but on 2 occasions after a 15 mile drive and stopping for 15 min., it wouldn't start, wouldn't engage the starter. The battery is good, connections are tight and clean, all lights, radio, AC fan, seats, etc., work, but when you turn the ignition key on, nothing happens, dead, no sound at all. After 20-30 min. it starts like nothing ever happened. I don't know if it's related to the heat under the engine compartment (works when cools off a little?), or to a faulty clutch interlock switch, or to the starter solenoid failing, or to the starter failing. Anyone else ever have this happen or have an idea of cause. It's hard to find the cause when you try it and it works, easier after it fails. Very annoying.