Ice wedge polygons on the North Slope of Alaska have been forming for many millennia, when the ground thermally contracts in the winter and water fills in the cracks during the snowmelt season. The infiltrated water then freezes and turns into ice. In this paper we investigate temperature dynamics around the ice wedges and surrounding permafrost. A 2-D nonlinear heat equation with phase change is utilized to compute temperature across the ice wedge and surrounding area. Thermal properties of the ground material are estimated by assimilating temperature measurements in the center of ice wedge polygons. The developed finite element model is successfully validated using two analytical solutions and tested in the case of ice wedges located in the tundra area near Barrow, Alaska, where a good agreement between the observed and computed temperatures is obtained. We demonstrate that in order to model temperature dynamics in the ice wedge, the water content above the ice wedge needs to be increased.