facts from Germany
I'm just giving my experiences and knowledge to that topic.
In the Olde Days, I found in books and have heard during my childhood time (1960s), women instisted on a hot rinse first (mostly with SIL, which was a rinsing agent with STTP, brightening agent and oxygen-bleach [sodiumperborate] and is still available but as a stain-remover like oxy-clean today) to get out the soap better, as soap can set in cold water, it was said.
This rinse was followed by a second warm rinse in clear water and finally one or two cold rinses were given to the washing until water stayed clear.
Usually the process-water from the hydraulic washing-machine motor was used for the 1-2 final rinses so no extra water was needed and the "coppers" in Germany often had a backboiler at the escape tube or had a double mantel with water in which was warmed during the boiling cycle without any extra fuel.
So far the information from the Olde Days.
On the other hand I found out that when using soap and when I do a rinse with hot water first, the tub or sink in which I do it is covered with a thin layer of scum (except if I put in soda) wheras this does not or not so much come up, if I do a cold rinse first and a warm or hot finally.
I tried the same with dishes, especially glasses, and had the same experiences with the kitchen-sink's and the glasses' surfaces.
So far to soap and soap-based powders.
Industry experimented with petro-tensides to avoid all these disadvantages especially as German automatic washers usually do not have connections to hot-water supplies but only have cold-water connections and so only cold rinsing is taking place in automatic machines here.
It is said that modern tensides and detergent-components rinse out even better in cold water than in warm water because warmth activates them better, a fact which is not helpful during the rinsing-out process.
Next thing to be kept in mind is that any hot or warm rinsing needs twice as much energy as cold rinsing and is bad for the environment! Here in Germany there is no machine on the market available that can do warm or even hot rinses since the end of the 1950-60 when soap-based powders disappeared from the market; there are some "eco-powders" on soap basis still available though but they are compound to rinse out in cold water as well as petro-detergents do.
Until some years ago I made my own soap (bar-soap and bath-soap) and also washed my clothes with it and found out that soap or soap based powders really make much softer washing than "chemical" powders do. Maybe it has something to do with very small quantities of fat-acids which are left over on the surfaces of the fibres and which work as a smoothener but do not hamper the water-absorption as conditioner's surfactants (kationic sufactants) do; to me that's also the reason why people started complaining about harsh washing in the 1960s when detergents were switched to petro-tensides instead of soap and conditioners appeared on the market.
Concerning terry-towels I found another hint to get them really smooth, fluffy and soft a few years ago in a laundry-book: as to the book towels should be rinsed in cold water first and finally in a warm, soft water (rain-water would be best they postulated) and not spun but hung up dripping wet on a line, then turned over after a while to make them dry more evenly and when only damp, the towels should be shaken out vigorously and then dried completely. When dry a second vigorous shaking before the laying will give them the final finish: smoothness, fluffiness and volume like on their first day.
Last but not least there's another fact which is not to be neglected:
washing in a tub-washer ALWAYS produces less harsh washing because the tumbling action in a FL scrumbles and tangles the fine fibres much more into eachother, folding and knotting their loose extensions together and therefor producing the so called "dry-stiffness" which has nothing to do with water-hardness because this can be seen when rinsing with a final "vinegar-rinse" (1/2 - 1 cup for a full load) and still towels come out quite harsh when dry afterwards.
So, that's all I know! Hope it helped a bit, too and wasn't too much to read!?
Ralf
