The induction of mild hypothermia, lowering body temperature by 4°C, is gaining acceptance as an acute therapy for the treatment of hypoxia and ischemia following cardiac arrest and many life-threatening injuries. When hypothermia is used following ischemia (as opposed to before ischemia), it needs to be performed rapidly for the greatest benefit, preferably within 5 min. When we consider the basic heat-transfer problem and define the engineering parameter space, we find that almost 3900 W of cooling are required in order to achieve 4°C cooling within 5 min. A simple model reveals that this poses a significant bioengineering challenge as the rate of heat transfer is severely limited, owing to a relatively confined fundamental parameter space. Current methods of cooling include external cooling devices, such as cooling blankets or ice bags, which are simple to use, relatively inexpensive but slow. Internal cooling has the best ability to cool more rapidly but current devices are more invasive, costly and most are still not able to provide cooling within the rapid 5-min interval. Cardiopulmonary bypass and recirculating coolants can achieve the cooling rate but are currently extremely invasive and require a highly skilled team to implement. Future therapies may include phase-change coolants, such as microparticulate ice–saline slurries or evaporative cooling technologies specifically designed for human use. With continuing research and investment, methods for rapid cooling can be developed and will translate into saving lives.