My Micra Sputters When Starting With A Hot Engine

Hello everyone, hope you can help me with this.

I have a Nissan Micra K11 1.0 16 valve from '95. I'm starting to notice some problems when I start the car, when the engine is warm.

If I start the car in the morning or when the engine is totally cooled down, it runs perfectly. But if I drive it for a while, stop the engine, and wait for it to cool down a little, the car sputters and runs very bad in neutral.

If I begin to drive it, after I have started it up, it will sometimes stall when I go into neutral. Then I have to start it again. To keep it from stalling, I have to keep the revs up, and this stops after 5 minutes, when the engine is fully warm again.

I have tried to change the fuel filter, but it was no help. Do you have any idea what it could be?