Vital signs have been essential clinical measures. Among these, body temperature (BT) and heart rate (HR) are particularly significant, and numerous studies explored their association in hospitalized adults and children. However, a lack of in-depth research persists in children admitted to the pediatric intensive care unit (PICU) despite their critical condition requiring particular attention. Objective: In this study, we explore the relationship between HR and BT in children from 0 to 18 years old admitted to the PICU of CHU Sainte-Justine Hospital. Methods: We applied Machine learning (ML) techniques to unravel subtle patterns and dependencies within our dataset to achieve this objective. Each algorithm undergoes meticulous hyperparameter tuning to optimize the model performance. Results: Our findings align with prior research, revealing a consistent trend of decreasing HR with increasing patient age, confirming the observed inverse correlation. Furthermore, a thorough analysis identifies Gradient Boosting Machines (GBM) implemented with Quantile regression (QR), as the most fitting model, effectively capturing the non-linear relationship between HR, BT, and age. Through testing the HR prediction model based on age and BT, the predictive model between the 5th and 95th percentiles accurately demonstrates the declining trend of HR with age, while HR increase with BT. Based on that, we have developed a user-friendly interface tailored to generate HR predictions at different percentiles based on three key input parameters : current HR, current BT, and patient's age. The resulting output enables caregivers to quickly determine whether a patient's HR falls within or outside the normal range, facilitating informed clinical decision-making. Thus, our results challenge previous studies' presumed direct linear association between HR and BT.