Not only you're not alone, this is a rather common physics experiment (or should be), but it doesn't have much to do with density - it doesn't change fast enough with temperature. But there is something about water that changes rapidly as you go from cold to hot water: viscosity.
Water's viscosity decreases rather dramatically with temperature - about 25% per 10deg C or so. The Reynolds number, a key descriptor of the fluid flow in a given situation, is inversely proportional to viscosity, with factor 1. Thus, in the flow of water in the tap, as you go from "cold" (around 10C) to "hot" (around 60C), the Reynolds number increases by a factor of ~3.5. In the turbulent flow, such a change is easy to hear.