Warm Water Rinsing
It was common to have at least one or two hot rinses, followed by several warm or cool/cold when doing laundry with soap, by the 1970's when detergents had nearly totally replaced the former, (tap) cold water was recommended to save energy. This was largely for domestic laundries and you can see this taking hold as fewer and fewer washing machines were sold with "warm/warm" or "hot/warm" cycles.
Commercial laundries in the United States by and large use central hot water supplied from a boiler and mixed at point of use for proper temperature. The other option is to use steam supplied from a central system to raise water temps to the required level.
Using centrally supplied water allows faster through-put as there is no time lost waiting for water to heat. It also makes possible warm water rinses as the machine is plumbed to both hot and cold water.
For commercial laundries there are several reasons why they would use warm water for rinsing. The first is that again given various local climates *cold* water could be very chilly indeed. That would leave laundry "cold" and thus more energy is required of the ironers or dryers. How much more energy probably has been factored out and available to those whom need it. Consumer Reports long as stated that while placing laundry rinsed in cold water into a tumble dryer increases energy use for the latter, it is still cheaper than using warm water rinses.
Natural textile fibers much like other things expands and contracts in relation to temperature. Warm and hot water rinsing in theory allows greater removal of chemicals and soils than cold. Again this is going to vary by local water temps and other factors such as chemicals used in the laundering process.
Historically American commercial laundries use chlorine bleach for whites and or colourfast loads. This is usually done in a separate cycle (first rinse) at hot water temps (>120F) and proper pH (alkaline) levels. Hot water not only causes a faster reaction time of cholorine bleach, it also causes much of the substance to gas off which helps to reduce the residue in fabrics. My guess is that following a hot (>140F) wash with a hot bleaching cycle with a cold rinse would not only cause textile shock but suddenly cause fibers to clamp down trapping soils, bleaches, residues etc to be trapped.
There is also the fact various chemicals added to the succession of rinses (anti-chlor, fabric conditioners/softeners, starches, etc...) dispense and or work better in warm to lukewarm water.
Finally remember reading somewhere that warm water loads are easier for washing machines to spin/extract since they are "lighter" than cold. One assumes this relates to evaporation rates and the ease of moving water at one temp versus the other.
One has tried warm water rinses on several loads in the Miele and notice more "gunk" is rinsed from the wash faster than with cold. Also the machine seems to ramp up to spin faster. Also laundry felt "dryer" at cycle end and yes they did tumble dry faster. Regarding wrinkles, didn't notice anything unusual and things came out of the dryer looking the same as when rinsed in cold.