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The extent to which the eddy statistics of the Martian atmosphere can be inferred from the mean state and highly simplified assumptions about diabatic and frictional processes is investigated using an idealized general circulation model (GCM) with Newtonian relaxation thermal forcing. An iterative technique, adapted from previous terrestrial studies, is used to generate radiative equilibrium temperatures such that the three-dimensional time-mean temperature fields of the idealized model match means computed from the Mars Analysis Correction Data Assimilation (MACDA). Focusing on a period of strong Northern Hemisphere eddy activity prior to winter solstice, it is found that the idealized model reproduces some key features of the spatial patterns of the MACDA eddy temperature variance and kinetic energy fields. The idealized model can also simulate aspects of MACDA's seasonal cycle of spatial patterns of low-level eddy meridional wind and temperature variances. The most notable weakness of the model is its eddy amplitudes-both their absolute values and seasonal variations are quite unrealistic, for reasons unclear. The idealized model was also run with a mean flow based on output from the Geophysical Fluid Dynamics Laboratory (GFDL) full-physics Mars GCM. The idealized model captures the difference in mean flows between MACDA and the GFDL Mars GCM and reproduces a bias in the more complex model's eddy zonal wavenumber distribution. This implies that the mean flow is an important influence on transient eddy wavenumbers and that improving the GFDL Mars GCM's mean flow would make its eddy scales more realistic.