Thank you very much for your answer Jim.

I am sorry that I did not express myself clear enough.
The starter motor runs fine, regardless if the engine is hot or not.

What I tried to explain was that when the engine is hot it will not start by using the starter motor (even though it cranks fine), but the strange thing is that it it starts (after about (5-6 revs) when I push-start it downhill. The latter situation may cause the engine to be run faster then the start motor manages, but I dont think that is the reason.

Any idea as to what can cause this problem ?
Electronic or mechanic ?
Any idea what to try to narrow down the problem ?

I would be grateful for any answer !