What you see that you call heat. Is actually the expansion of the atmosphere. As heat causes particles to be more energized (well that's what heat is, energy) those particles move around more, and the forces (gravity) holding them together become more over powered. Thus the particles become more spread apart.
So heat = particles spreading apart because of it energizing AKA expansion.
Now when see this in the atmosphere, whats happening is that light going through the heated area is being magnified (from the way gravity is effecting the photons passing through the less dense area). Which causes that 'heat' look.
This is why when the sun is around the horizon especially on a hot day, tends to look bigger. It also gets redder because the light is weakened as it passes through more atmosphere (the light itself looses energy).
Now in video games/realtime applications they use sharers and particles that have a black and white image (kinda like a hightmap, initially rendered separately) that determine which areas of the image should be magnified and which shouldn't. In ray tracers and path tracers, they try to simulate light a little more realistically by casting rays through an area which is "heated" or in other words has an algorithm that causes the rays to spread out or to be magnified.
ENSONIQ5 used meta balls as his heated areas and had set the properties of it to magnify the light simulating in a heated area.
Unfortunately doing this type of thing in anim8or at the moment would be either too much work, or too slow or both. Especially when there is software out there made for doing that sort of stuff (also FREE ones too!).
