  $W_{N,k}$ minimal models possess an interesting class of `light' primaries
which control much of the low energy density of states in the large $N$ 't
Hooft limit. In this paper we conduct a detailed exploration of their
distribution using a combination of numerical and analytical techniques. We
also make some observations about the density of states of the full CFT. Our
results appear to support the contention that there is no finite temperature
analogue of the Hawking-Page transition in these systems.
