Permafrost degradation in ice wedge polygon terrain has accelerated in the last three decades, resulting in drastic changes to tundra hydrology which may impact rates of soil organic carbon mobilization. The goal of this research was to determine how surface topography influences ground temperatures in ice wedge polygons, thereby influencing the vulnerability of the underlying permafrost. The central hypothesis is that energy preferentially enters the subsurface in summer at low, wet zones (such as low-centered polygon centers and troughs), then is released to the atmosphere in winter through elevated zones (such as rims). Disturbance to the balance between these seasonal fluxes can help explain the onset and development of thermokarst. We constructed a model of thermal hydrology in ice wedge polygons using the Advanced Terrestrial Simulator (ATS), a state of the art code that couples a meteorologically drive surface energy balance with equations for subsurface conservation of mass and energy. The model was first calibrated against a year-long record of ground temperature throughout the subsurface of a low-centered polygon near Prudhoe Bay, Alaska. We then explored the sensitivities of ground temperature, active layer depth, and laterally-oriented subsurface heat fluxes to surface topography, by repeating simulations with systematic alterations to rim height and trough depth. Our results suggest that rims operate as preferential outlets of subsurface heat in winter, causing the ground to cool more efficiently. The destruction of rims and sinking of troughs associated with high-centered polygon development increases winter ground temperatures at the periphery of the polygon, possibly impeding ice wedge cracking. Ice wedge degradation can be sustained by positive feedbacks, because troughs deep enough to host perennial thermokarst pools sustain thicker active layers. The results expand upon and quantify current conceptual models of thermokarst development and shed light on non-linear changes to Arctic hydrology driven by climate change.