The ECU temp sender is made to run the car richer when its cold, meaning every ones golf would run like his when cold...?!? I cant see it making that much diffrence, i would exepect the engine to idle higher and loose economy but not to the point where it runs that badly and actualy smells of fuel.
The Air temp sender is built into the air flow metre, it could be either of them, the Air flow metre is measuring out the fuel/air ratio depending on how much air is taken into the engine, if its reading wrong.. your fuel mix will be wrong, hence having bad economy and running issues, ultimatly you would be overfueling to the point where it tryes to stall. the air temp sender is also adjusting the fuel mix. they are both built into the AFM so would be replaced together.
Which then leads on to the lambda sensor, which is effectivly the other end of the air flow metre, the AFM measures how much has gone in and the lambda meansures how much is going out. So if the lambda is saying the o2 content is very low, the ECU will adjust the fueling to alow more power to the engine, and yes it does increase emissions but its ok as long as its within the lambda range. So if yours is reading wrong it will alow to much fuel into the engine and the lambda is not correctly telling the ECU to lean out the fuel mix.
So... Could be either of those two.
... other things as said before is the fuel pump relay..Its normal for these to click if the engine is about to stall or has stalled etc.. When the engine drops rpm it shuts off the fuel, if the engines happens to fire again it will click on to bring the engine back to life. Also would not explain your fuel smell and bad economy.
Here is a list of other potentual causes of your problem
Air Filter
Air Intake system/vaccume system - leaks/blockage
ECT (engine coolent temp sensor)
Fuel pressure/delivery rate/pressure regualtor
Closed throttle position (CTP) Switch
Injectors
Mass Air flow sensor (MAF) aka AFM
Intake air temp snesor (IAT)
heated oxygen snesor (HO2S)
Exhaust system/catalytic convertor
ECM (Engine control module)
Idealy you need to get your car on diagnostics, rather can fork out for new ECUs and AFMs when all you needed was a relay or something
