The study of the thermal response of ice covered streams to an effluent of high temperature, or of fast moving water, has been of considerable interest to those concerned with hydraulic systems, environmental effects, and navigational routes in cold regions. The discharge of tributary thermal effluents into cold region rivers may alter the thermal and hydrodynamic conditions of ice cover progression and create reaches of open water in the ice throughout the winter season. An analytical approach, based on pertubation techniques, has been developed and tested concerning the suppression of ice cover and the migration of its fronts. The upstream and the downstream ice edges are determined for two cases of steady non-uniform flow. Conditions for the suppression of the ice cover are also obtained based on the relative positions of the upstream and downstream ice edges. Comparison with field data shows a good agreement with the formulation incorporating the thermal effluent velocity.