The Antarctic and the Southern Ocean region are well known for environmental fragility and harshness, which may pose unprecedented risks to shipping traffic. However, novel and innovative technologies continue to prepare vessels better than ever to cope with harsh polar conditions. The Antarctic and the Southern Ocean are also coupled with the abundance of marine resources and possibilities for economic activity, which has led to considerable international attention and the implementation of rules and guidelines in an effort to conserve and protect both human life and the polar ecosystem. Most prominent amongst these is the International Code for Ships Operating in Polar Waters, adopted by the International Maritime Organisation (IMO), in order to better regulate the operation of vessels within the Antarctic region. This thesis considers the winterisation process of the MV-Bluefin's, a research vessel, in the context of the vital seawater (SW) cooling system, which transfers waste heat away from the operating systems to better assist the vessel in withstanding the harsh climatic conditions. Calculated for a grid of two-dimensional weather vectors - SW temperature as the first coordinate and air temperature as the second - the MV-Bluefin's power demand may exceed the generators' available power supply as a direct result of the extreme temperature fluctuations. The aforementioned failure probability is added to the vessel's standard failure risk. Two models have been developed as part of this thesis for assessing such risk. The first model distributes the extreme weather vector according to a truncated bi-normal distribution. The power risk is analytically derived as the integration of the probability density function (PDF) over the critical region, identified as the weather vector area where the power failure is expected to occur. Conversely, the second model divides the vessel's mission into an arbitrary number of segments. Each segment consists of several days with the daily weather vector distributed according to a segmented truncated bi-normal distribution. Thus, the power risk is derived through a computer simulation of 10,000 pseudo-missions and is only considered successful if all weather vectors fall outside the critical region. The power risk is calculated for both models as a function of ambient temperatures. It estimates the level of risk according to the specific vessel dynamics, human factors within a confined space, and a variety of operational and environmental factors, thus providing an early warning for vessel operators and being used to assist in real-time decisions throughout vessel missions. In the case of the MV-Bluefin, the simulation observed the probability of the system indicating a warning which increased concurrently with the likelihood of the vessel experiencing a power risk, thus allowing for appropriate preventative and mitigative measures to be taken.