All the available ISO (black points) and Herschel (red points) observations of H₂O  (left panel) and CO (right panel) lines for T Tau are shown. Left panel: line fluxes predicted by a slow C-shock for an emitting area of  ~360 AU diameter and pre-shock density of n = 10⁶ cm^-3  (velocity V = 20−30 km s^-1, solid lines), or n = 10⁷ cm^-3  (V = 10−20 km s^-1, dotted lines). The low-excitation water lines are well reproduced by C-shock with pre-shock density of 10⁶ cm^-3  while the higher excitation lines require higher pre-shock density. Right panel: CO line fluxes predicted by: a C-shock model (n = 10⁶ cm^-3, V = 20−30 km s^-1, emitting area diameter, D = 360 AU, red line); an LVG warm gas component (n = 10⁶, T = 300 K, D = 360 AU, N_CO = 1.5 × 10¹⁸ cm^-2, blue line); the sum of the two models (green line). While the high-J CO lines are well reproduced by the same C-shock model used for water lines, a warm gas component is required to simultaneously fit the lower-J lines observed with ISO (down to J_up = 14).