Context. Most of the mass in protoplanetary disks is in the form of gas. The study of the gas and its diagnostics is of fundamental importance in order to achieve a detailed description of the thermal and chemical structure of the disk. Both radiation from the central star (from optical to X-ray wavelengths) and viscous accretion are the main sources of energy, dominating disk physics and chemistry in its early stages. This is the environment in which the first phases of planet formation will proceed.Aims. We investigate how stellar and disk parameters impact the fine-structure cooling lines [Ne II], [Ar II], [O I], [C II], and H2O rotational lines in the disk. These lines are potentially powerful diagnostics of the disk structure, and thei...