Question

how do the characteristics of heated and cooled air change the movement of air

Answer 1

When air is heated, the molecules gain kinetic energy and begin to spread out. The air therefore becomes less dense which is why hot air rises, and vice-versa for colder air.

Answer 2

global wind pattern is best example of effect of temperature change of wind. energy always flow from higher to lower region so this way global wind pattern changes and as @cj7529 has explained the concept of decreasing air density is also a good example