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The classical Kuiper belt contains objects both from a low-inclination,presumably primordial, distribution and from a high-inclination dynamicallyexcited population. Based on a sample of classical TNOs with observations atthermal wavelengths we determine radiometric sizes, geometric albedos andthermal beaming factors as well as study sample properties of dynamically hotand cold classicals. Observations near the thermal peak of TNOs using infra-redspace telescopes are combined with optical magnitudes using the radiometrictechnique with near-Earth asteroid thermal model (NEATM). We have determinedthree-band flux densities from Herschel/PACS observations at 70.0, 100.0 and160.0 $\mu$m and Spitzer/MIPS at 23.68 and 71.42 $\mu$m when available. We haveanalysed 18 classical TNOs with previously unpublished data and re-analysedpreviously published targets with updated data reduction to determine theirsizes and geometric albedos as well as beaming factors when data qualityallows. We have combined these samples with classical TNOs with radiometricresults in the literature for the analysis of sample properties of a total of44 objects. We find a median geometric albedo for cold classical TNOs of 0.14and for dynamically hot classical TNOs, excluding the Haumea family and dwarfplanets, 0.085. We have determined the bulk densities of Borasisi-Pabu (2.1g/cm^3), Varda-Ilmare (1.25 g/cm^3) and 2001 QC298 (1.14 g/cm^3) as well asupdated previous density estimates of four targets. We have determined theslope parameter of the debiased cumulative size distribution of dynamically hotclassical TNOs as q=2.3 +- 0.1 in the diameter range 100<D<500 km. Fordynamically cold classical TNOs we determine q=5.1 +- 1.1 in the diameter range160<D<280 km as the cold classical TNOs have a smaller maximum size.

"TNOs are Cool": A survey of the trans-Neptunian region X. Analysis of classical Kuiper belt objects from Herschel and Spitzer observations