Hot-start problems are indicative of loss of pressure in the fuel line. This is usually caused by a leaky fuel injector.
The reason why this happens only for hot starts is because the fuel is more likely to vaporize as temperature increases.
In order to avoid vaporization problems the fuel lines are expected to be pressurized during a hot start.
If there is a fuel leak then the fuel may have partially vaporized by the time it reaches the fuel injectors, preventing the injectors from sending fuel through to the combustion chambers.