Unless you have a cite from a manufacturer, I will claim that manufacturers do not suggest letting the car warm up for a few minutes. Anyone who wants the straightest dope possible can consult the owner’s manual in the glovebox of their own car.
I let my car idle for maybe twenty seconds before driving away - and I only wait that long because it idles oddly if I touch the gas pedal before that point.
The amount of heat that goes into the engine components is approximately proportional to the mechanical power being delivered by the engine. In other words, if the engine makes more power, it will warm up faster. OTOH mashing the pedal to the floor before pistons and cylinders are up in their normal operating temperature range is likely to cause damage. Best advice is to start it, let it stabilize for maybe ten seconds, and then drive away in a moderate fashion; just take it easy on the gas pedal for the first mile or so.