hi all i just bought a polo and its got a fault with it

well here goes

when i jump in the car in the morning and try and start the car it just wount fire up,, i have changed the battrey on it and its still the same

it turn over and the battrey ok,, it trys to start but it just wount,, its no the starter by the way lol,,
when its cold as i said it wount start bump if i bump start it then its all ok, smokes for about a min or 2 and a little rought when cold aswell

but

when its warm it starts 1st tirn every single time.. and runs sweet as a nut

im hoping this is not expensive to fix but some 1 told me it can be the

blue top coolent temp sensor in the distributer cap,, this will not allow the fuel/air to mix to go correctly or summin and they are only about £10 from vw.. please can u help shane