Think of gas in a container, but not as some sort of continuous substance, but as it really is, a bunch of molecules moving every which way, colliding off of each other all the time, etc. If you take average kinetic energy of a molecule, then that is basically what temperature is.
The same is true for solids, particles may be confined from moving about, but they can still vibrate in their place in the substance so they still have kinetic energy.
Coldness is simply lack of heat, less motion, less kinetic energy, means less temperature.
That’s also why there is absolute zero, you can’t have negative kinetic energy, absolute standstill is the slowest you can go. Due to quantum uncertainty principle, even that is not actually achievable.
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