starts OK when cold, hard start when warm.

2006 jetta brm,
the car starts very well when the temp is -23C (-9F) but it would almost not crank after a short 20 min ride or after the engine is warm.
If I cycle the glow plugs 2 times and wait 3-4 secs the car starts after a hesitation.
Before i go buy a new starter do any of you have any advice on what else should I check? which ground points should I check?
the battery is good, at cold the car starts at first engine spin.
thank you very much!!

Fuel filter.
Do you hear the lift pump run for a second or two under the passenger side rear seat when you switch the key to ON?

no joy?!

Have you replaced your fuel filter?

Can you hear the pump?

Thank you for your answer,
yes, I can hear the fuel pump and the fuel filter was changed 6000 miles ago.
It's not that the engine cranks and does not fire.
My problem is that the engine will not crank when warm! after searching the forum - it could be the starter or grounding points,
thank you