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Context. The determination of the physical conditions in molecular clouds is a key step towards our understanding of their formation and evolution of associated star formation. We investigate the density, temperature, and column density of both dust and gas in the photodissociation regions (PDRs) located at the interface between the atomic and cold molecular gas of the NGC 7023 reflection nebula. We study how young stars affect the gas and dust in their environment. Aims. Several Herschel Space Telescope programs provide a wealth of spatial and spectral information of dust and gas in the heart of PDRs. We focus our study on Spectral and Photometric Image Receiver (SPIRE) Fourier-Transform Spectrometer (FTS) fully sampled maps that allow us for the first time to study the bulk of cool/warm dust and warm molecular gas (CO) together. In particular, we investigate if these populations spatially coincide, if and how the medium is structured, and if strong density and temperature gradients occur, within the limits of the spatial resolution obtained with Herschel. Methods. The SPIRE FTS fully sampled maps at different wavelengths are analysed towards the northwest (NW) and the east (E) PDRs in NGC 7023. We study the spatial and spectral energy distribution of a wealth of intermediate rotational 12CO 4 ⩽ Ju ⩽ 13 and 13CO 5 ⩽ Ju ⩽ 10 lines. A radiative transfer code is used to assess the gas kinetic temperature, density, and column density at different positions in the cloud. The dust continuum emission including Spitzer, the Photoconductor Array Camera and Spectrometer (PACS), and SPIRE photometric and the Institute for Radio Astronomy in the Millimeter Range (IRAM) telescope data is also analysed. Using a single modified black body and a radiative transfer model, we derive the dust temperature, density, and column density. Results. The cloud is highly inhomogeneous, containing several irradiated dense structures. Excited 12CO and 13CO lines and warm dust grains localised at the edge of the dense structures reveal high column densities of warm/cool dense matter. Both tracers give a good agreement in the local density, column density, and physical extent, leading to the conclusion that they trace the same regions. The derived density profiles show a steep gradient at the cloud edge reaching a maximum gas density of 105-106 cm-3 in the PDR NGC 7023 NW and 104-105 cm-3 in the PDR NGC 7023 E and a subsequent decrease inside the cloud. Close to the PDR edges, the dust temperature (30 K and 20 K for the NW and E PDRs, respectively) is lower than the gas temperature derived from CO lines (65-130 K and 45-55 K, respectively). Further inside the cloud, the dust and gas temperatures are similar. The derived thermal pressure is about 10 times higher in NGC 7023 NW than in NGC 7023 E. Comparing the physical conditions to the positions of known young stellar object candidates in NGC 7023 NW, we find that protostars seem to be spatially correlated with the dense structures. Conclusions. Our approach combining both dust and gas delivers strong constraints on the physical conditions of the PDRs. We find dense and warm molecular gas of high column density in the PDRs. [ABSTRACT FROM AUTHOR]