I work in a secure office park, and I can use my spare key to lock the car, so I’m not concerned about theft (plus I have insurance). I want my car to be nice and warm when I leave the office in the evening, or if I want to run out and get a cafe-mocha-double-expresso. I asked around the office about fuel consumption, and the only source I’d consider even remotely authoritative said a gallon an hour. That sounds like a lot - but he’s no Celil Adams. I was thinking more like a gallon all day. By the way, I drive a new Honda Accord Sedan with a 4-cyl motor (for your calculations).
So, from half a gallon to a gallon per hour times 10 hours as Jim noted could be anywhere from 5 to 10 gallons. Yeah, that could be half the tank, depending on the car. You want to pay 20 bucks a day in order to have a warm car when you leave work?
This site says that idling for more than 10 seconds burns gas twice as fast as an average speed moving vehicle (whatever speed that is). Another site says idling uses 1/2 to 1 gallon of gas an hour. I think you’re definitely best off not leaving it idling all day from a cost perspective, to say nothing of the amount of harmful emissions.
Look into getting a remote start installed. Besides being a bad idea, it is horrible on your engine to let it idle for long periods of time. The oil presure is at it’s lowest point, the coolant circulation is not as good, etc. It basically puts a lot of unnecessary wear on your engine.
So spend that money on a remote start kit, or give the $15 you would spend to have your car idling all day to a co-worker or something. Heck, I will glady start your car for you for $15!
As described in this thread, I locked the keys in my truck with the engine running a few years ago, and it burned slightly under two gallons in about two and a half hours.