How limescale forms

Limescale is calcium carbonate coming back out of solution. Heating is what does it, which is why kettles and heating elements scale and cold pipes generally do not.

The reaction: Ca(HCO₃)₂ → CaCO₃ (solid) + CO₂ (gas) + H₂O. Heat drives it to the right.
Why only temporary hardness scales: Only bicarbonate-associated hardness decomposes on heating. Sulphate and chloride hardness stays in solution.
Removal: Descaling with a weak acid — citric or acetic — dissolves it back. Softening prevents it by removing the calcium first.

Text description

Hard water contains dissolved calcium and bicarbonate. When heated, bicarbonate decomposes into carbonate, carbon dioxide and water. The carbon dioxide escapes as gas, and the carbonate combines with calcium to form solid calcium carbonate, which deposits on the hottest surfaces. A scaled heating element transfers heat less efficiently and uses more energy for the same result.