(abridged) Spectral energy distributions (SEDs) were constructed for a sample of 477 classical cepheids (CCs). The SEDs were fitted with a dust radiative transfer code. Four stars showed a large mid- or far-infrared excess and the fitting then included a dust component. These comprise the well-known case of RS Pup, and three stars that are (likely) Type-II cepheids (T2Cs), AU Peg, QQ Per, and FQ Lac. The remainder of the sample was fitted with a stellar photosphere to derive the best-fitting luminosity and effective temperature. Distance and reddening were taken from the literature. The stars were plotted in a Hertzsprung-Russell diagram and compared to evolutionary tracks for cepheids and theoretical instability strips. For the large majority of stars, the position in the HRD is consistent with the instability strip for a CC or T2C. About 5% of the stars are outliers in the sense that they are much hotter or cooler than expected. A comparison to effective temperatures derived from spectroscopy suggests in some cases that the photometrically derived temperature is not correct and that this is likely linked to an incorrectly adopted reddening. In this work the presence of a small NIR excess, as has been proposed in the literature for a few well-known cepheids, is investigated. Firstly, this was done by using a sample of about a dozen stars for which a mid-infrared spectrum is available. Secondly, the SEDs of all stars were fitted with a dust model to see if a statistically significant better fit could be obtained. The results were compared to recent work. Eight new candidates for exhibiting a NIR excess are proposed, solely based on the photometric SEDs. Obtaining mid-infrared spectra would be needed to confirm this excess. Finally, period-bolometric luminosity and period-radius relations are presented for samples of over 370 fundamental-mode CCs.
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