Which outer solar system satellites have sub-surface oceans is an important geophysical and astrobiological question. We developed a technique that translates a moon’s long-wavelength topography (Nimmo et al. 2011) into an inferred heat flux distribution, indicating whether there is a rigid or liquid layer beneath the ice shell (Beuthe 2013). Our technique independently detects Titan and Enceladus’ sub-surface global oceans and finds moment of inertia (MoI) and heat flux estimates consistent with past results (Iess et al. 2010; Nimmo & Bills 2010; Iess et al. 2014). Here we focus on Tethys (for which gravity information is lacking) and infer a normalized MoI of 0.33 and no ocean. We find a present-day surface heat flux of 1.1 mW/m2 that implies either a highly dissipative interior or a higher obliquity than predicted (Chen et al. 2014). To translate topography into tidal heating, we first remove the effects of tidal stretching and rotational flattening—a function of the moon’s MoI. We then invoke isostasy (constant pressure at depth per Hemingway & Matsuyama 2016) to translate the residual topography into tidal heating, approximated as basal heat flux under the ice shell. As tidal heating only varies in spherical harmonic degrees 2 and 4, we only translate the topography of these degrees. The inferred variation in basal heat flux necessary for surface topography depends on the assumed average basal heat flux as well as whether we assume Pratt (density-variation-driven) or Airy (buoyancy-driven) isostasy. We only expect a sub-surface ocean with Airy isostasy. Finally, we perform a multi-linear regression upon the basal heat flux distribution to characterize it in terms of the weights of three basis functions (Beuthe 2013) that describe spatial variations in tidal heating, and subsequently if there’s an ocean. We explore the parameter space of average basal heat flux and MoI to determine the best-fit interior, and check density profiles for viability. We conclude that Tethys undergoes Pratt isostasy and obliquity tides. Our best-fit model of Tethys’ internal structure is a 66 km thick layer of porous ice, atop 165 km of solid ice, with an ice/rock core of 300 km radius. We have also applied the model to Mimas but will need to use a numerical tidal code to determine which of two conflicting results is more likely.