You need N joules to heat up the 300kg of the engine. It doesn't matter if you sit there for 15 minutes freezing your ass with an engine running at 1500rpm (and all other car parts still freezing) or 5 minutes actually driving at 3000rpm - you still spent N joules on heating, difference is the time. And the car heater runs on the engine heat, not on the electricity, so the sooner you would warm the engine the sooner your car interior start to warm and stops seeping the heat from engine.

It's actually more importantly to have enough viscosity in ATF, but again, the sooner you would go the sooner it would warm.

Because it’s much more efficient to heat up a modern car by driving it than it is to let it idle.

> I’m curious about that recommendation, do you know why that is?

I was always told (since the 90s, anyway) that it's better to drive off slowly with a cold engine and let all the components come up to operating temperature together than to drive off with a hot engine, and cold gearbox, driveshafts, tyres, etc.

I generally let a cold engine (i.e. overnight) idle for maybe 30s before driving off slowly, and it reaches operating temperature in about 5m or less.

Because your car engine does not get the right mixture until you start driving.

In a 2022 car I have now even the cabin doesn’t get proper heating from the aircon until it’s driven.