The gas temperature structure of protoplanetary disks is a key ingredient for interpreting various disk observations and for quantifying the subsequent evolution of these systems. The comparison of low- and mid-J CO rotational lines is a powerful tool for assessing the temperature gradient in the warm molecular layer of disks. Spectrally resolved high-J (Ju> 14) CO lines probe intermediate distances and heights from the star that are not sampled by (sub-)millimeter CO spectroscopy. This paper presents new Herschel/HIFI and archival PACS observations of 12CO, 13CO, and C ii emission in four Herbig AeBe disks (HD 100546, HD 97048, IRS 48, HD 163296) and three T Tauri disks (AS 205, S CrA, TW Hya). In the case of the T Tauri systems AS 205 and S CrA, the CO emission has a single-peaked profile, likely due to a slow wind. For all the other systems, the Herschel CO spectra are consistent with pure disk emission and the spectrally resolved lines (HIFI) and the CO rotational ladder (PACS) are analyzed simultaneously assuming power-law temperature and column density profiles, using the velocity profile to locate the emission in the disk. The temperature profile varies substantially from disk to disk. In particular, Tgas in the disk surface layers can differ by up to an order of magnitude among the four Herbig AeBe systems; HD 100546 is the hottest and HD 163296 the coldest disk in the sample. Clear evidence of a warm disk layer where Tgas>Tdust is found in all the Herbig Ae disks. The observed CO fluxes and line profiles are compared to predictions of physical-chemical models. The primary parameters affecting the disk temperature structure are the flaring angle, the gas-to-dust mass ratio, the scale height, and the dust settling.