We simultaneously analyze the spectral line energy distributions (SLEDs) of CO and H₂ of six local luminous infrared (IR) Seyfert galaxies. For the CO SLEDs, we used new Herschel/SPIRE FTS data (from J = 4–3 to J = 13–12) and ground-based observations for the lower-J CO transitions. The H₂ SLEDs were constructed using archival mid-IR Spitzer/IRS and near-IR VLT/SINFONI data for the rotational and ro-vibrational H₂ transitions, respectively. In total, the SLEDs contain 26 transitions with upper level energies between 5 and 15 000 K. A single, constant density, model (n_H2 ~ 10^4.5−6 cm^-3) with a broken power-law temperature distribution reproduces well both the CO and H₂ SLEDs. The power-law indices are β₁ ~ 1–3 for warm molecular gas (20 K<T< 100 K) and β₂ ~ 4–5 for hot molecular gas (T> 100 K). We show that the steeper temperature distribution (higher β) for hot molecular gas can be explained by shocks and photodissociation region (PDR) models; however, the exact β values are not reproduced by PDR or shock models alone and a combination of both is needed. We find that the three major mergers among our targets have shallower temperature distributions for warm molecular gas than the other three spiral galaxies. This can be explained by a higher relative contribution of shock excitation, with respect to PDR excitation, for the warm molecular gas in these mergers. For only one of the mergers, IRASF 05189–2524, the shallower H₂ temperature distribution differs from that of the spiral galaxies. The presence of a bright active galactic nucleus in this source might explain the warmer molecular gas observed.