This study is a randomized controlled trial conducted at Beijing Anzhen Hospital, Capital Medical University. The primary objective is to assess the efficacy of mild therapeutic hypothermia in reducing infarct size and improving cardiac function in patients receiving percutaneous coronary intervention under venous-arterial extracorporeal membrane oxygenation for acute myocardial infarction complicated with cardiogenic shock. Secondary objectives include evaluating the safety of mild therapeutic hypothermia and its impact on venous-arterial extracorporeal membrane oxygenation weaning success and short-term survival.