Simple answer. No.
Today’s cars use electronic fuel injectors, which rigorously control the amount of gas delivered to the engine when you hit the ignition. As a result, virtually no fuel is wasted during startup, and only a thimbleful is burned as the car roars to life. So forget about the 30-minute axiom you were raised on—the threshold at which it makes more sense to shut off rather than to idle should be expressed in seconds, not minutes.
How many seconds, exactly? A lot of environmental organizations advocate the 10-second rule: If you’re going to be stopped for more than 10 seconds, it’s best to shut off your engine. The one exception is when you’re stopped in street traffic—it’s illegal to kill the engine in many states, due to concerns that switched-off cars are more easily rear-ended (especially if an absent-minded driver forgets to restart once the gridlock abates).
. . . The researchers concluded that restarting a six-cylinder engine—with the air conditioner switched on—uses as much gas as idling the same car for just six seconds.
Idling is similarly wasteful in frigid temperatures. Contrary to popular belief, cold-weather drivers needn’t warm up their cars for longer than 30 seconds. The best way to raise an engine’s temperature to optimal levels is to drive it almost immediately after startup . . .