We report observations of the CO J = 7 \rightarrow 6 transition toward the starburst nucleus of NGC 253 . This is the highest-excitation CO measurement in this source to date , and allows an estimate of the molecular gas excitation conditions . Comparison of the CO line intensities with a large velocity gradient , escape probability model indicates that the bulk of the 2–5 \times 10 ^ { 7 } ~ { } M _ { \odot } of molecular gas in the central 180 pc is highly excited . A model with T \sim 120 K , n _ { H _ { 2 } } \sim~ { } 4.5 \times 10 ^ { 4 } ~ { } cm ^ { -3 } is consistent with the observed CO intensities as well as the rotational H _ { 2 } lines observed with ISO . The inferred mass of warm , dense molecular gas is 10–30 times the atomic gas mass as traced through its [ C ii ] and [ O i ] line emission . This large mass ratio is inconsistent with photodissociation region models where the gas is heated by far-UV starlight . It is also not likely that the gas is heated by shocks in outflows or cloud-cloud collisions . We conclude that the best mechanism for heating the gas is cosmic rays , which provide a natural means of uniformly heating the full volume of molecular clouds . With the tremendous supernova rate in the nucleus of NGC 253 , the CR heating rate is at least \sim 800 times greater than in the Galaxy , more than sufficient to match the cooling observed in the CO lines .