Hot air is less dense, which is why it rises. This density disparity is also why you can sometimes “see” the heat. Rays of light refract (bend) as they go from one substance to another, the effects of which are also visible when you look at things under water. In this case, the two “substances” are the hot air and the cooler air. Light is bent as it moves from one temperature of air to another, because it travels faster in the hot air than the cold. Thus, you see a weird shimmering in the air because the light is getting bent all different ways. This is also why you can see the shadows of the air currents.
More on refraction here and here.