The shape of the water heating device, and the act of heating the water causes mini bubbles to form. The pressure in the pipes prevents the bubbles from coalescing.
Just because the water is 30C hotter than the cold doesn’t mean it suddenly gets bubbly. The geyser/furnace needs to impart the gas to the hot water.
Not every house the hot water is cloudy, it depends on the specific geyser/furnace/pipes.
Water out the kettle for your tea is not cloudy, no pressure to keep in the minibubbles.
There are two types of flow, [laminar and turbulent](https://www.cfdsupport.com/OpenFOAM-Training-by-CFD-Support/node334.html). Laminar flow is nice and smooth, while turbulent flow sloshes around and is rougher. As temperature increases, flow becomes more turbulent. This causes the hot, turbulent water to loosen some of the deposits off the inside of the pipes and nozzle, which get carried out with the water.
Source: Heat Transfer professor explained why hot water is cloudy.
It appears that calcium carbonate (limestone), a mineral, is less soluble in hot water than in cold water, so it precipitate in particules making hot water cloudy.
Not ELI5: this is due to the higher solubility of CO2 in cold water, allowing an acido-basic reaction equilibrium with calcium carbonate to a chemical form more soluble in water.
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