FIAT PUNTO 188 Start problems / Warm condition

Hello engine community I have a problem with my Punto. The car only starts when the engine is cold. If I drive a few KM and the engine is warm I have problems with the start. The engine tries to start. So it stutters. And that unfortunately always when it is warmed up. Can not use the car at all. I have to say that I am a big layman. When afforesting various forums I encountered the problem very often. Unfortunately no one has noticed the problem. Most suspected the source of the fault: temperature sensor crankshaft sensor/pulse sensor Problems onboard computer with the immobilizer When it is warm, it starts when it is pushed on. Cold it starts without any problem. Spark plugs have only been changed. ÖL too, but with me the ÖL-lamp still lights up. Did someone have a similar problem that I can describe to the workshop? At the first inspection, the nic was able to hts find. Spark plugs have been changed. Would be very happy about help. I don’t have money for new car at the moment. The reperatures scare me already. The battery has also been changed. However, this has only 40ahm. But that’s probably not the problem in my opinion.