We revise the physical conditions in the O++ zone of the planetary nebula NGC 6543, obtaining two different estimates of the electron temperature (Te) and one estimate of the electron density (Ne). The electron temperature is computed by means of two independent methods, the nebular-to-auroral ratio [O III] λ5007/λ4363 and the diagnostic diagram that combines λ5007 with the [O III] infrared lines at 52 and 88 μm. The optical and infrared fluxes have been obtained from archival HST/WFPC2 images and ISO Long Wavelength Spectrometer spectra, respectively, and the continuum intensity in the optical has been measured from narrow-slit spectra obtained with the Isaac Newton Telescope at La Palma. The measured continuum intensity is higher than predicted by recombination theory under the hypothesis that all the Lyα photons either escape or are destroyed. This fact can be explained in terms of an enhancement of the two-photon continuum due to Lyα conversion, a process that depends strongly on the local structure of the nebula. Alternative possibilities, outside the framework of recombination theory, have also been considered, e.g., the optical tail in the X-ray emission of a very hot plasma, and dust scattering of stellar radiation, but these hypotheses are not supported by quantitative estimates. While the electron temperature and density derived from the diagnostic diagram agree with the most recent determination, the temperature derived from λ5007/λ4363, Te(O++)opt, is somewhat smaller than previously published values. We discuss several technical issues that contribute to the overall uncertainty in our results, focusing on the instrumental effects that might bias the [O III] λ4363 intensity. We also discuss the effects of the collisional de-excitation of the O++ ground terms on the relation between Te(O++)opt and Te(O++)IR. Based on observations with ISO, an ESA project with instrument funded by ESA member states and with the participation of ISAS and NASA.