We have studied the central regions of the planetary nebulae A 30 and A 78 by UBVRI photometry, optical spectroscopy, and near-infrared photometry. The spectra contain high-excitation emission lines and strongly resemble those of Wolt-Rayet stars of the carbon sequence. We infer stellar temperatures > 50,000°K. The observed 3.5-ym flux of each nebula exceeds reasonable extrapolations of both the stellar flux and any possible free-free emission. The colour temperature of this excess between 2.28 and 3.5 /im is ∼ 1000°K. For each nebula, the aperture dependence of the excess emission suggests an extended (y10 arc-sec radius) region centred on the nucleus. Thermal radiation from a distribution of dust that is concentrated near the nuclei seems the most plausible explanation for the excess, but no theory of dust formation or heating seems totally adequate at present. (Paper will appear in the Monthly Notices of the Royal Astronomical Society.)