Shifts from deep to moderate hypothermic circulatory arrest (HCA) in aortic arch surgery necessitate an examination of their differential impacts on neurocognitive functions, especially structured verbal memory, given its significance for patient recovery and quality of life. This study evaluates and synthesizes evidence on the effects of deep (≤20.0 °C), low-moderate (20.1–24.0 °C), and high-moderate (24.1–28.0 °C) hypothermic temperatures on structured verbal memory preservation and overall cognitive health in patients undergoing aortic arch surgery. We evaluated the latest literature from major medical databases such as PubMed and Scopus, focusing on research from 2020 to 2024, to gather comprehensive insights into the current landscape of temperature management during HCA. This comparative analysis highlights the viability of moderate hypothermia (20.1–28.0 °C), supported by recent trials and observational studies, as a method to achieve comparable neuroprotection with fewer complications than traditional deep hypothermia. Notably, low-moderate and high-moderate temperatures have been shown to support substantial survival rates, with impacts on structured verbal memory preservation that necessitate careful selection based on individual surgical risks and patient profiles. The findings advocate for a nuanced approach to selecting hypothermic protocols in aortic arch surgeries, emphasizing the importance of tailoring temperature management to optimize neurocognitive outcomes and patient recovery. This study fills a critical gap in the literature by providing evidence-based recommendations for temperature ranges during HCA, calling for ongoing updates to clinical guidelines and further research to refine these recommendations. The implications of temperature on survival rates, complications, and success rates underpin the necessity for evolving cardiopulmonary bypass techniques and cerebral perfusion strategies to enhance patient outcomes in complex cardiovascular procedures.