The aging of water is an old, traditional method of water preparation. Before there were good, effective dechlorinators, aging allowed the chlorine in the tapwater to evaporate (outgas, actually). Nowadays, when water supplies typically contain chloramine, aging is useless for this purpose. A dechlorinater/conditioner must be used. These conditioners work instantaneously; so their is no practical reason to age water in this day and age.
As for temperature-matching. Use a thermometer for a while; eventually you'll learn to judge temperature by touch. This is close enough. If your refill water is a few degrees cooler than the tank water, it will be as though a rainfall has cooled the paddy or pool. Your fish will likely start looking around for a mate.