Why aren't any jet fuels heavier than Jet A/A-1/JP-8 in common use? The commonly-used jet fuels fall into two main categories:


Straight kerosenes (Jet A, Jet A-1, JP-8, JP-5, plus, historically, JP-1), which are used in most situations because their high flashpoints make them safer to handle.
Gasoline-kerosene blends (Jet B, plus, historically, JP-3 and JP-4), which are used in very cold climates due to their lower freezing points, but are much more dangerous to handle due to their very low flashpoints.


However, even the straight kerosenes have flashpoints below 40C, which can easily be exceeded in hot-weather operations, potentially with lethal results.  Using a fuel with a somewhat heavier composition (and, thus, a higher flashpoint) would greatly alleviate this danger; for instance, the lighter diesels have flashpoints in the 50C-60C range, and would, thus, seem to be a safer choice than kerosene-based fuels for hot-weather operations (especially in tropical and subtropical climates where very hot weather is more common than elsewhere), where their higher freezing points would not be an issue.

So why aren't there any "heavy" jet fuels for hot-weather use?
As @john K said, fuel needs to be liquid at cruising altitude. The less volatile a hydrocarbon is at a temperature, the quicker it will stop flowing as the temperature drops. 

Additionally, the plane is not necessarily landing in the same hot climate it is taking off from. You need a fuel that is stable across the range of temperatures experienced while operating.

This post addresses the specific behavior of different fuels in great depth.