Hard X-ray spectra of 28 bright Seyfert galaxies observed with INTEGRAL were analysed together with the X-ray spectra from XMM–Newton, Suzaku and RXTE. These broad-band data were fitted with a model assuming a thermal Comptonization as a primary continuum component. We tested several model options through a fitting of the Comptonized continuum accompanied by a complex absorption and a Compton reflection. Both the large data set used and the model space explored allowed us to accurately determine a mean temperature kT e of the electron plasma, the Compton parameter y and the Compton reflection strength R for the majority of objects in the sample. Our main finding is that a vast majority of the sample (20 objects) is characterized by kT e < 100 keV, and only for two objects we found kT e > 200 keV. The median kT e for entire sample is 48 $_{-14}^{+57}$  keV. The distribution of the y parameter is bimodal, with a broad component centred at ≈0.8 and a narrow peak at ≈1.1. A complex, dual absorber model improved the fit for all data sets, compared to a simple absorption model, reducing the fitted strength of Compton reflection by a factor of about 2. Modest reflection (median R ≈ 0.32) together with a high ratio of Comptonized to seed photon fluxes point towards a geometry with a compact hard X-ray emitting region well separated from the accretion disc. Our results imply that the template Seyferts spectra used in the population synthesis models of active galactic nuclei (AGN) should be revised.