The term "heat lightning" is one that you probably grew up hearing, took to be true, and never really questioned the meaning of. I remember being little and seeing lightning in the distance that was unaccompanied by thunder, and hearing the term "heat lightning" tossed around.
Well, friends, I am here to dispel the rumor and set the record straight that there is no such thing as "heat lightning". If you see lightning in the distance but do not here any thunder, you are just too far away from the storm for the sound waves to reach you! The sound waves that are thunder cannot travel nearly as far as the light from lightning can. The sound waves will usually dissipate after a few miles. The exact distance will depend on the atmospheric conditions, but usually the range is no more than 10 miles. Depending on what the terrain setup and atmospheric conditions are, the sound wave can even be blocked (by mountains) or refracted (change direction) before it reaches your ears. Air of different temperatures (and densities) can actually refract the sound waves away from you in certain instances.
On the contrary, lightning can be seen, under ideal conditions, about 10 times farther away than it can be heard - around 100+ miles! This would be under extremely ideal conditions however (flat terrain, clear skies, high cloud tops) and so the more common range for lightning to be seen would be around 50-70 miles. Either way, the lightning that you are seeing is still being followed by thunder, the sound waves just aren't reaching you! Sometimes, the storms look much closer than they actually are, and so you may think for sure you'd be close enough to hear thunder. Over the past few weeks I have witnessed a lot of these distant storms that have been 40-60 miles away from my viewpoint in Lynchburg, even though they appear much closer.
One final note- debris in the atmosphere can also cut down the range in which thunder can be heard, and this is what I believe happened the night of the Derecho. Many noted, including myself, that although there was vivid lightning that little to no thunder was heard. Because of all of the heavy sand and dust that was flying through the atmosphere picked up by the storm, the thunder was muffled to a point that you probably didn't hear it unless the strike was within a mile or two of your location. The same thing can also happen during thundersnow.