Seems to just mean geting the scope to match the ambient temperature, at least as best or close as you can. Will say that if it takes an hour to "cool down" then the scope does not get that before I start observing.
Reason is simply that the choice seems no observing to observing but not at "perfection". Since with my eyes perfection is not going to happen I observe whenever I can. Having slight astigmatism means I can happily think "So what?"
Usually the scope goes out, bits gets found and taken out, scope gets set up and aligned and checked then I select a target and get observing. probably the scope gets 20 minutes cool down maybe 30. But I am not going o wait another 30-40 minutes.
Having a goto however means that during the late afternoon (still light) I can take scope out, attach power, level it, point North and then cover and leave it until dark to align. Saves trying to do it all in the dark. In this case the scope gets one or two hours cool down.
It does mean that the scope needs to match the ambient temperature to provide the good views. There are two issues, as the optics are cooling, they can change shape, not a good thing. Secondly, when the optics are warmer than ambient, there are convection currents in the tube, these are like mini-mirages or bad seeing so looking through these "tube currents" blurs the view at the eyepiece.
How important thermal equilibrium depends on the size and type of telescope. Small telescopes generally cool faster than large telescopes and refractors are much less sensitive to thermal issues. Based on my experiences here in the mild climate of San Diego, I think it's very unlikely that a 10 inch Telescope without active cooling (a fan cooling the mirror) will be close to ambient in an hour. Even with effective cooling, it will take an hour..
Certainly one can observe with a telescope that has not cooled down to ambient, with larger scopes it's probably rare that they are fully cooled. At low powers, the effects are minimized and may not be visible, where it is important is at higher magnifications when viewing the planets and splitting close double stars.
Realistically, your eyes would have to be very poor for the views of the planets and doubles to not be affected by a cooling scope. Slight astigmatism generally disappears as the magnification is increased because the small exit pupils only uses a small portion of the eye lens..
To get the best our of a larger scope, attention must be paid to getting it cooled down. At the 200 inch at Palomar, they keep the observatory cooled to what they believe will be the outside temperature during most of the night..
And ambient, it's a moving target, on clear nights, the temperature drops over the course of the evening so the ability of the telescope to track the air temperature is important.