The application of polymer flooding is currently under investigation to control water cut and recover residual oil from a giant sandstone reservoir in Kazakhstan, where the water cut in most producers exceeds 90%, leaving substantial untouched oil in the porous media. The primary objective of this research is to explore the feasibility of a novel approach that combines the mechanisms of mobility control by polymer injection and the thermal effects, such as oil viscosity reduction, by utilizing hot water to prepare the polymer solution. This innovative hybrid method’s impact on parameters like oil recovery, resistance factor, and mobility was measured and analyzed. The research involved an oil displacement study conducted by injecting a hot polymer at a temperature of 85 °C, which is higher than the reservoir temperature. Incremental recovery achieved through hot polymer injection was then compared to the recovery by conventional polymer flooding and the conventional surfactant–polymer-enhanced oil recovery techniques. The governing mechanisms behind recovery, including reductions in oil viscosity, alterations in polymer rheology, and effective mobility control, were systematically studied to comprehend the influence of this proposed approach on sweep efficiency. Given the substantial volume of residual oil within the studied reservoir, the primary objective is to improve the sweep efficiency as much as possible. Conventional polymer flooding demonstrated a moderate incremental oil recovery rate of approximately 48%. However, with the implementation of the new hybrid method, the recovery rate increased to more than 52%, reflecting a 4% improvement. Despite the polymer’s lower viscosity during hot polymer flooding, which was observed by the lower pressure drop in contrast to the conventional polymer flooding scenario, the recovery factor was higher. This discrepancy indicates that while polymer viscosity decreases, the activation of other oil displacement mechanisms contributes to higher oil production. Applying hybrid enhanced oil recovery mechanisms presents an opportunity to reduce project costs. For instance, achieving comparable results with lower chemical concentrations is of practical significance. The potential impact of this work on enhancing the profitability of chemically enhanced oil recovery within the sandstone reservoir under study is critical.