Photometric observations from 1.6 to 3.5 mu of 28 planetary nebulae are presented. Most of these emit 3.5- mu radiation in excess of that expected from thermal emission by ionized gas. When combined with the measurements of Willner, Becklin, and Visvanathan, the data show that the nebulae with relatively high densities are the more likely to emit excess 3.5- mu radiation. This trend supports a model in which the excess radiation arises from dust particles that cool off as the nebulae evolve. (auth)