Amit,
Am very amazed at this strange phenomenon as i have never seen or
heard anything like this happening in any car. Its dangerous too as
our Linea's brakes and steering are powered and when car switches off
they would loose their full efficiency too.
Did you fill fuel from a different pump this time? The best thing
would be to go to TASS asap, get teh ECU scanner hooked up and it
would throw some error code (mail FIAT beforehand) if the ECU scanner
doesnt throw any error code then a lot of physcial checks would be
required.
Either your Idling RPM is messing up or fuel problem- highly unlikely
as you say otherwise its fine.
These cars are so technologically advanced, we can just make guesses.
Hope your Linea gets fine asap.