Vauxhall Vectra trouble starting from cold

I'm having trouble starting my car from cold.
When I try to start it from cold it turns over for ages before starting.
There is usually a big puff of white smoke too.
I've put in a new starter motor and had checks done from 2 garages and they found nothingu.
I did manage to discover that when I turn the key the light on the dash only stays on for about a second so I traced it back to the coolant temperature sensor.
When I disconnect the coolant temperature sensor the light stays on for ages, goes off, and the car starts first time perfectly.
so I changed the CTS and still have the same problem.
Please help because I look stupid having to go under the bonnet every time it want to start my car
Thanks