You're kidding right? Thermal inertia? LOL Heat has no mass. You must be an engineer! I had always assumed that hot water froze before cold water because the former has a much lower concentration of dissolved gases. Cold water with it's dissolved nitrogen, oxygen and CO2, to name the main gases, behaves as a eutectic solution that exhibits a freezing point depression. In college, I was the top student in Physical Chemistry - loved it.