Rotax 582

These are textbook symptoms of a fuel vapor lock.

The hot engine heats the fuel lines to over 50°C and the volatile fractions of the fuel "Boil", forming a vapor bubble in the fuel lines.

The engine-driven fuel pump is inefficient at pumping gases and the engine won't start on the vapors.

Sometimes extended cranking will clear the vapors but you risk burning up the starter.  This still applies if it is Pull-Start and the starter is you! 

Keeping it cool is a quick answer.  You might try leaving the Oil Access door in the cowl OPEN to vent the heat.

If you have a battery, an Electric AUXillary Fuel Pump installed close to the fuel tank and at the lowest/coolest point you can get it, would allow you to purge the fuel lines before starting the engine.

The 582 is on a Streak Shadow so the engine is not enclosed, but I will take on board what you are saying. Always grateful for good advice.  Thank you 

Then I would ask, "Are the fule lines in insulating Fire Sleeving?

Is the fuel line routed above/near the cylinders or under the engine?

I see that this aircraft model has high wings but low mounted fuel tanks.

Is your aircraft equipped with an Electric Fuel Pump? And is it running when it won't restart?

No, the fuel pipes are situated below the engine and it has the standard fuel pump that operates from the pressure from the crank case. They are not covered so it's all a bit strange. Not sure what you mean "Does it start when running?"  Will have a closer look and take your advice.  Thanks

Just read it again and understand what you are asking -you are referring to the electric fuel pump which it doesn't have :o)