Fiat Punto power problems for first 5 mins of driving

Hi everyone,

I would really appreciate any advice you can give me. I have no idea about cars, so please reply in the simplest terms possible!!

After my car over-heated last December, for the first few minutes of driving my punto I have to floor the accelerator to get it to move. It has cut out once or twice while I've been driving, and is very jumpy. Even though you can hear the revs, the power doesnt always get through. After a few minutes the problem goes, and it drives fine.
I've taken it to a garage, and the guy said it was bubbles in the radiator/cooling system, so he bled it and replaced a fuse for my cooling fan as that was also down. It still had issues, so I took it back and he said it was the fuel pump. This was also replaced, and again I'm still having these issues. He now says it is the air sensor. I've also had another garage say it is the cold start valve??

As you can tell, I have no clues about cars and have to trust other peoples opinions, but I'm getting fed up with this guy guessing the problem and me having to pay to fix something that is not causing this.
It does this whether it is a cold morning or not, and still does it when I leave it idle for a while before driving, although it is not as severe It starts without problems. Any advice would be greatly appreciated :)