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Fever can provide valuable information for diagnosis and prognosis of various diseases such as pneumonia, dengue, sepsis, etc., therefore, predicting fever early can help in the effectiveness of treatment options and expediting the treatment process. This study aims to develop novel algorithms that can accurately predict fever onset in critically ill patients by applying machine learning technique on continuous physiological data. We analyzed continuous physiological data collected every 5-minute from a cohort of over 200,000 critically ill patients admitted to an Intensive Care Unit (ICU) over a 2-year period. Each episode of fever from the same patient were considered as an independent event, with separations of at least 24 hours. We extracted descriptive statistical features from six physiological data streams, including heart rate, respiration, systolic and diastolic blood pressure, mean arterial pressure, and oxygen saturation, and use these features to independently predict the onset of fever. Using a bootstrap aggregation method, we created a balanced dataset of 7,801 afebrile and febrile patients and analyzed features up to 4 hours before the fever onset. We found that supervised machine learning methods can predict fever up to 4 hours before onset in critically ill patients with high recall, precision, and F1-score. This study demonstrates the viability of using machine learning to predict fever among hospitalized adults. The discovery of salient physiomarkers through machine learning and deep learning techniques has the potential to further accelerate the development and implementation of innovative care delivery protocols and strategies for medically vulnerable patients.