Not sure I understand this. Water for a water change should be relatively close to the temperature of the tank water. A few degrees cooler is OK, in fact I usually do this deliberately, as it will stimulate the fish and spawning overnight is frequent. When preparing to treat ich you can increase the temperature of the replacement water a few degrees to help raise the overall tank temperature. In both of these situations, we are talking a few degrees, and it is not going to be rapid fluctuation. The latter can seriously affect fish.
Fish are ectothermic. Temperature as in all animals drives the metabolism, so with fish this temperature is that of the water they live in. Once this temperature is outside that in which the fish's metabolism is designed to function at its best, the fish begins to have issues. At the very least, this is putting stress on the fish, and there could also be internal organ issues, osmoregulatory problems, etc.