The cooling system is probably getting old ... but to leave a car idling for 15 min is not a good practice for the car or for your gas milage.
possible radiator resrtiction
to hotcheck your cluch fan or if elec. make sure their working
clean rad & cond at the car wash see if that wont help
Check and see if the fan cluch is good. Your fan. At higher speeds, the fan is not needed due to the high airflow. At low speeds and idle, you need the fan to operate to cool the car.
Thermostat regulator is malfunctioning, water pump pulley could be bad, gas bubble in radiator hose.
When driving the IAC does not do anything because the car is not at an idle
To give more info, the car surges before it dies. I can actually keep the car running if I tap the accelerator when I feel it surge. The car also dies at idle. I don't know if this is related or not, but the car easily overheats even with new coolant and thermostat.
If it overheats at speed, but cools down when you slow down, the problem is likely a head gasket. Combustion gasses are leaking into the cooling system, adding bubbles (which take the place of coolant) and extra heat. Slowing down means the engine is spinning slower, and less combustion gas gets into the cooling system.
Assuming the car is a gas powered vehicle, and not a diesel the answer is, just long enough to get all the snow off the windshield. You don't need to let the car idle before driving it. The only reason to let it idle before driving is to defrost/defog the windows.
Each car overheats at a different temperature you need to look up and find out on the internet
make sure there's enough coolant in the radiator.