The excitation energy dependence and temperature dependence of photoluminescence from boron nitride nanotubes and hexagonal BN powder samples are reported. The results are discussed within a model attributing the broad 3.2 eV luminescence from these samples to self-trapped excitons in the low-dimensional structures of BN nanotubes and of nano-arch surface reconstructions on h-BN sheet edge faces in powder. An empirical model accounting for the unusual combination of excitation and temperature dependence of photoluminescence seen in these measurements is suggested. For the model to be consistent with the hypothesis of self-trapped excitons on BN nanotubes, it may be necessary to show that the cores of multiwall nanotubes are selectively probed by light tuned below the h-BN exciton.