Hi Cannon,
Does your car use Bosch k-Jetronic fuel injection? I had a Mk2 16V Golf with a similar problem some years ago. Try the following:
1. Locate the fuel distribution / metering device (it will have reinforced hoses going to the injectors, and when your car won't start, give the device a sharp tap in the top-centre. The metering piston is directly below this casting and mine used to stick in the down position when hot therefore not allowing any fuel to be injected. A sharp tap would usually free it up. If this fails, take the air intake cover off and move the circular disk up and down several times. This should move very smoothly - any stickiness indicates a problem with the piston bore and the unit will need replacing.
The use of a good fuel injector cleaning solution will help keep this free.
2. Another possibility is the cold-start regulator. This is bolted to the engine block and, depending on temperature, varies fuel pressure to the top of the piston I mentioned in (1) above. Unbolt it thereby letting it cool down when you have the problem and see the engine starts. Don't leave it un-bolted though becuase your engine will run rich.
all the best
Jon
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