Car will not start when hot?

The car listed above is a Super Beetle with auto stick. The car runs flawlessly with no issues except, when the engine is hot, 25 mile or so drive, the car will not start. When you turn the key there is no sound, no solenoid clicks no starter whir just the sound of silence. Once the car cools off, usually for an hour or more, turn the key and she starts first time and purrs like a kitten. Could the neutral safety switch be the culprit? We are seniors in a remote area of North Carolina. Please help us. Thank you.