I maybe able to help?
I spent nearly 20 years in engine powertrain R&D, oil temp' is the benchmark for a warmed thru engine, its a shame so few cars have an oil temp gauge now
Leaving the car idling is just about the worst way to warm your engine thru bar just keying on and going flat out just as the car catches and 1st fires
. Before the F1 anoraks say something else, I worked for Cosworth and Honda F1 and race engines have their own set set of rules, but still rely on a warm up lap which in part is still to warm the engine thru, amoungst brakes and simple shakedown.
Leaving the car to idle means it will take a very long time to warm the engine thru and it may never get there if the it's a cold day.
So just start and drive with mechanical sympathy to get that engine warmed, nay normally and the engine will warm thru with minimal damage, with the thermostat doing it's job by restricting coolant flow to speed up the process until correct coolant temp regulates it.
Cold starts are what wear the engine, and it's incredibly disproportionate which is the best reason for using premium oil
I have owned many cars with 200K+ miles, and driven manufacturers durability cars with 600K+ and all running excellent engines (even Land Rover's!) these engine haven't been subjected to little runs around town which kills the both the oil and the engines with so many cold starts.
hope this helps