When it's cold, it's going to take longer than 30 seconds for all cylinders to even be firing and oil to flow, nevermind trying to drive!
Most of my stuff isn't even hitting great on all cylinders in 30 seconds, never mind ready to move when it's cold. Easily a good 20-30 mins to get some heat into the engine and it making a semblance of power.
High idle is fine. But that's ~1000-1200 rpm. Std idle around 600-700rpm. 2500 is getting up there on revs for alot of engines.
Of course "warming up" at 30* is much different than at -30*, or colder.