Theories with anomalies exhibit unusual thermodynamic and hydrodynamic behavior. This behavior may be captured entirely by constructing a "thermal" anomaly polynomial which encodes the solution to the Wess-Zumino consistency condition and an additional condition (consistency with the Euclidian vacuum) which the thermodynamic partition function must satisfy. Using the thermodynamic partition function, the role of the anomaly in hydrodynamics can be traced to the coefficients of certain Chern-Simons terms on the base manifold over which the thermal circle is fibered.