But unless your car is over 30 years old, it will almost certainly have electronic fuel injection rather than a carburettor. Fuel injection doesn't need the right temperature for a car to run smoothly - the fuel-air adjustment is all taken care of automatically and the car will run nicely right from start-up. Modern oils are also very good at circulating freely until the vehicle has reached optimum operating temperature.
But there's still no harm in a bit of a warm-up, right? Wrong.
Cars pollute more when they are cold and the quickest way to warm them up is to drive. Idling at any temperature is a waste of fuel because the engine is running and you're not going anywhere. You can't get worse fuel consumption than that.
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So the longer you idle when cold, the more fuel you waste. Pretty simple.
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Even if you don't have angst about fuel use and emissions, a winter warmup could also be damaging your car. When an engine is cold, the fuel injection system compensates by injecting a richer fuel mixture so that it runs smoothly. But fuel is a solvent and some of that extra can find its way in the cylinder walls, washing precious lubricant away and reducing the life of components.
The best way you can look after your engine is to get it up to operating temperature quickly. That's not to say you spin the wheels and hit the redline the moment you're out the driveway; you still need to drive conservatively to protect your car for 5-10 minutes, or until it's up to temperature. But moving away as soon as possible is still the kind and eco-friendly thing to do.