If you drive a car from 1970, you should probably warm it up for a few minutes before driving in the wintertime, as the carburetor needs to be warm to work well. But if you have a car without a carburetor -- i.e. something from the 21st century -- warming up your car for any longer than 30 seconds is a tremendous waste of time and gas.
As the U.S. Department of Energy points out, the engine will warm up more quickly if it's being driven. And since the car's heater works off engine heat, that means you'll warm up faster too.
When it comes time to cool off a car that's been baking the sun on a scorching hot day, popular wisdom says it's best to roll down the windows for a few minutes while blasting the AC. That's true, but there are two other important steps to take as well.
The first is to make sure the AC vent is blowing fresh outside air rather than recirculated car air. The second is to set the AC so it hits downward toward your feet as well as in your face. This will quickly push out the broiling air trapped in the lower part of the car and you can roll those windows up even faster.