This solubility behavior accounts for most of the noise your teapot makes before the water reaches its boiling point . Air that was dissolved in the cold water can't stay there as the temperature rises, and it bubbles loudly out of solution. By the time the water itself is hot enough to vaporize rapidly, most of the dissolved gases have left. This solubility rule applies only to solids that are stable in the presence of water.
Calcium chloride is unstable in the presence of water.
When mixed with water, most of the crystals do dissolve, releasing heat. Those that don't dissolve incorporate water molecules into their solid lattice, four to each calcium atom. O dissolves better in hot water than in cold. And, of course, it would be useless in a hot pack.