Like with many things in life, the answer is “It Depends”. In this case, it depends on two factors – what kind of display technology your monitor is using and how color-critical your tolerances are. Older technologies like CCFL, will move pretty dramatically during a warm up period, and it’s advised to let them warm up for ~30 minutes prior to calibration. More modern displays use WLED backlight and warm up faster, so it’s really a matter of your personal preference.
I have a consumer grade BenQ GW2780 (~$150) purchased in 2022. And I have a tool that allows me to measure my screen’s color temperature and luminance with a spectrophotometer, so I decided to measure how my screen changed over the course of an hour after being turned on. Not surprisingly, the color temp moved a bit, cooling off, during the first few minutes of operation, and then the change settled down to a pretty linear relationship with time, starting to decelerate during minutes 30-60. After an hour, it was pretty stable. 100K of movement can roughly be approximated to 1 ∆E (2000) of color difference, about the minimum amount detectable by the human eye.
So, to get back to the original question, if you are highly color-critical and your tolerances are in the 1 ∆E range, then you may want to let your screen warm up 30-60 minutes prior to calibrating. If you are more of a “regular” person, with a 2 ∆E tolerance, then you’d be fine calibrating after the screen is on for just a few minutes.
