1982 audi ur quattro with wr engine, after car has been running, then stopped for say 15 mins. The car cranks over for ages and when it starts it is choked up and missing it takes 20 seconds and then runs fine

 

One of the reason coming in my mind is Spark plugs, distributors, and ignition coils because they are the examples of parts that might be deteriorating or failing. These parts might not be able to provide a strong enough spark for ignition when the engine is hot.