Important considerations that must take place in the warm-up:
1. Increase of body temp. What's the gauge? I have no idea. I err on the side of sweat 'beads' on the forehead and sweat showing through on the athletes shirts.
2. Increasing specificity; specificity in terms of movement, neurological recruitment specific to loads and speeds to be used. We progress from general, starting with the easiest on the body (depending on some of the factors I will list out in a minute here), and moving to more specific. There has got to be specific movements, loads, and speeds geared towards to the highest intensity activity for the day, or injury at some point will be inevitable. The 5th or 6th rep of some sprint work should hopefully not be the pinnacle of motor recruitment for that day... if an athlete makes it that far without the sniper getting him or her; what about reps 1, 2, or 3? Do not waste reps continuing to warm-up. (you could use testing measures to mark peaks or falls in performance which can help guide training... another topic for another time)
I look at it as a pyramid; a slow ascend to allow time for the heating to move to the peripheral (helping with many things from oxygen's "stickiness to hemoglobin and nerve conduction velocity), potentiating motor unit recruitment, increasing extensibility of all tissues (maybe the wondrous fascial system won't be screaming for a foam roller or real soft tissue therapy from real hands as much; I am not saying soft tissue work is not useful or necessary from time to time, but being smart helps to not have to back track so much), time for capillaries to dilate and increase in enzyme activity among many other things.
3. Time; minus any adrenaline "bomb", the above processes take time and just "jamming" the transmission into overdrive can really take it's toll. It can be like an overuse injury, it may not show up tomorrow or even next month, but over the years the body will take a beating. Warm-ups do not and should not be marathons and take away precious time from the rest of training, but accuracy to do the right/necessary things is critical and one of the necessary things is time. Patience will pay off.
4. Utilize the warm-up with movements that can teach or enhance the learning of that days work; slower, less intense versions of the subsequent work hits on specificity and the rest time to wait for the physiological processes to take effect is a good time to teach lessons on anything that will help with training, today and throughout their career.
Recovery is just as much about the training and how one warm-ups has subtle effects that may make an athlete 'age' much faster. I know cryogenics can theoretically prolong life, but in terms of movement, being cold can strain body structures much more.
The coaching details I observe are breathing rates (I stand close enough to the athletes to hear their breathing); the first few faster drills/movements will require a little more time as the enzyme activity increases, capillaries dilate and the disassociation of oxygen slowly improves, being cognizant of mental states/mood (how is the athlete behaving today vs. other days; subtle body language/facial cues/reactions to you and others/etc.), what day of the week it is (athletes tend to get slight energy boosts towards the end of the week... *sometimes not though, and this could be a real potential indicator for some serious changes that need to be made), time of the day as circadian rhythms will effect hormones, body temp and other physiological processes, time of the year which can greatly effect the circadian rhythms with the upper latitudes experiencing greater diversity such as that here in Grand Forks, North Dakota; think about what it's like to warm-up at 6 am when body temp is usually near its lowest and the wind chill is -30 degrees F; and in the spring when temperatures drastically change warm-ups may be shortened to save from sapping energy the goals of each workout. But as the summer progresses, a heat acclimated body's cooling efficiency necessitates probably re-extension of warm-up volume. Other aspects such as individual personalities, times within the training season and on the school calender, and even motivation from team success factors can play a larger role than most might think.
Now these probably seem like a lot, and I don't have a 100 different warm-ups for every scenario, but I do make sure to tweak here and there with a few additional movements or added time to make sure that we are warm in the both physical and mental sense; or for some individuals, scrap parts of the training for the day. I am working on getting more objective measures for this type of stuff, but I still feel pretty confident with evolution's unlikely and amazing eye and ear. Hey... and developing a real strong relationship with the athletes helps quite a bit too; mom and dad can usually tell when something 'isn't quite right' with their son or daughter. That part of the collegiate environment is great because of the time to spend with the athletes, and any chance you get to spend time with them outside of the usual training and sport environment is time well spend, so long as it's genuinely getting to know each person better.
All of this falls under the umbrella of really trying to be aware of the setting and time given for training. Sequencing exercises within a workout, sequencing workouts to allow for precise recovery and so not to overload specific movements and systems to a point of slow or no return, understanding the "psychological stress" that different days of the week may present and there time within the year play a role covers a lot of ground to ensure both sides of the training/recovery street are kept moving as best as possible. Damage control is much easier when there is less damage to control.
This might be an elementary post on warming-up as there are so many factors to consider and reasons for certain warm-up routines and drills; even different perspectives on what to do and justifications for when and why that could be right in the certain contexts, but the bottom line here is maybe diligent warming-up can really save on the body acutely and long term... "easy on the transmission big fella".