While the responses are
slightly varied and if there is a common point, I'm reading Engine Oil Temperature as the true measure, not the clock. The Oil Temperature of that second engine, either fully off or a minimum idle, also seems to pass the Common Sense test. While the actual calculation of a time includes multiple other variables that are well above my pay grade, I particularly like @tdracer's note,
"At Boeing (where we want to minimize any unnecessary engine wear or deterioration prior to turning the aircraft over to the buyer) we use 5 minutes for both warm-up and cool-down.
Also remember, for warm-up during winter operating conditions (i.e. really cold) most engines have a minimum oil temp before setting high power." (Sorry, I could not find the quote button today.) Their use of
five minutes seems to meet all of the objectives as well as providing a simple number for line flying. I don't think any operating company will bitch about five minutes when the SOP may say three. And your mileage may vary.