Boxster 987 hot start problem

[JimVick]

My 2005 Boxster S always starts first time when cold.
When car is hot after a run and is started within 15-20 mins starts first time regardless of outside temperature.
When car is hot and left for an hour or so it is difficult to start
Will start straight away and then just slow right down and stop.
If I try again but give it some throttle it will try to stop and is very sluggish but if I keep it above about 1500 RPM for 2-3 seconds it seems to catch and then run normally.
Is worse in summer time when outside temperature is around 28-30 C.
If temp is around 20-20 C starts normally.
Any ideas?

[Ronpor]

Maybe the fuel pump.

[merc1963]

check the back flow valve inside the fuel tank