Also for the warmup case, tolerances inside the engine are designed assuming a hot engine. At lower temperatures, the metal hasn’t expanded yet causing also more stress on various parts such as the piston (seals).

And for the turbo I forget to mention that if you leave a turbo engine idle for a few minutes that this allows both the temperature and speed of the turbo to reduce. Many trucks have a sticker in the dashboard saying “do idle engine x minutes before shutdown to avoid turbo damage”. (But also do not idle for extended periods which I’m not 100% what’s the reason. I guess it’s due to diesel engines in some cases getting too cold while idling.)