We have analysed the XMM-Newton X-ray spectra of the yellow giant 31 Com with the aim of deriving information on the coronal structures of this archetypical Hertzsprung-gap star. To determine the emission measure distribution vs. temperature, EM(T), and the elemental abundances of the coronal plasma, with an accurate line-based approach, we have developed a new method for simple and accurate line measurements, based on rebinning and co-adding the two RGS spectra. We have reconstructed the EM(T) independently with both APED and CHIANTI atomic databases in order to investigate possible differences in the final outcome of the analysis, and we have obtained consistent results. The derived emission measure distribution has a well defined peak at T ˜ 107 K and a significant amount of plasma at higher temperatures; there is also evidence for plasma at temperatures below ˜106.5 K, with a mean electron density of ˜3 × 1010 cm-3, as inferred from the line ratio of the O Vii triplet. We have made a global fitting of the EPIC spectra, using multi-component isothermal (3-T) model, and then compared the results with the EM(T), looking for a consistent multi-temperature description of both the RGS and EPIC spectra, over the whole spectral range. While the EM(T) and the 3-T models individually provide a good description of the data set on which they are based, none of them describes adequately the data of all the other instruments; the disagreements may be related, at least in part, to cross-calibration problems. Finally, we have used the EM(T) to derive information about the properties of the coronal structures. Our results indicate that the corona of 31 Com is dominated by a class of magnetic loops with peak temperature ˜107 K and apparently more isothermal than the solar ones. Table 3 and Appendix A are only available in electronic form at http://www.edpsciences.org