Yes the reason I use engine temp is at least if thats hit warm then the oil has stood some chance of getting warmed enough to at least be some of the way to being "fluid" enough to deal with my right foot

I aint got oil temp yet but its in the pipeline along with some other guages and senors
Oh and its not just the O2 sensors that are the issue according to folk I have spoken to, its to do with what the cars "using" in terms of deciding fuel delivery. Eg open and closed loop. It is usually faster than 3 mins but depending on the car and other factors it can take longer than 30 seconds for a cold start MINI to "settle" and reduce the issue of surging under throttle when cold. It only really starts to disappear as the car gets nioce and warm...which takes abot 3-5 mins of tickover or gentle driving IMO from past experience. if you fire the car up and listen to it, you'll hear when it suddenly changes...the pitch of the engine changes as does exhaust note and smoothness of idle.