I let mine run for about 5 minutes with remote start if its below freezing. If it's below zero F I'll let it run for 15 minutes - Its really hard to drive when you can't move for the shivering
Above freezing and I'll start it with remote start as I walk towards it - It usually finishes the turbo test by the time I get to the drivers door, and I just drive away.
I have tried starting it and just driving immediately, but it puts out a huge cloud of brownish black smoke and retards the engine pretty severely for the first 15-20 seconds.
Also, in the summer time I turn the "Quiet Start" feature on - it makes it low idle if I do remote start it. In the winter I turn "Quiet Start" back off since it makes it high idle to warm up faster.