Warm Water Rinses
While indeed can give better results in rinsing for some items, is mostly a hold over from when soaps were used for wash day instead of detergents.
When using soap, the first few rinses were alwasy hot or at least warm to keep the textile fibers from contracting, thus trapping soils, dirt and soap residue (and scum for that matter), into the textiles. Since modern detergents soften water quite well, and when properly dosed in correct washing conditions soils and muck are kept away from laundry, warm water rinsing became less of an issue.
Being as that may, some commercial laundries, and even domestic housewives still use warm water for rinsing, for two reasons. One, as noted above it does keep textile fibers from contracting, thus allowing a flushing action to rid laundry of soils and detergent residue. Two, when going from a hot or very hot wash, it is not good to put certian fibers right into a cold rinse, as it can cause "shock", leading to some nasty creases. Finally the more chemicals one uses for the wash bath, and depending upon the number of rinses, warm water can give better results.
Remember also in the United States, what counts as "cold" water will vary by location and time of the year. Tap water in January in Maine or New York is going to be warmer than the same in Atlanta or Texas.
Only time one has ever used warm water rinses, is when trying to remove heavy detergent build up from laundry.