Non-invasive temperature monitoring of individuals plays a crucial role in identifying and isolating symptomatic individuals. Temperature monitoring becomes particularly vital in settings characterized by close human proximity, often referred to as dense settings. However, existing research on non-invasive temperature estimation using thermal cameras has predominantly focused on sparse settings. Unfortunately, the risk of disease transmission is significantly higher in dense settings like movie theaters or classrooms. Consequently, there is an urgent need to develop robust temperature estimation methods tailored explicitly for dense settings. Our study proposes a non-invasive temperature estimation system that combines a thermal camera with an edge device. Our system employs YOLO models for face detection and utilizes a regression framework for temperature estimation. We evaluated the system on a diverse dataset collected in dense and sparse settings. Our proposed face detection model achieves an impressive mAP score of over 84 in both in-dataset and cross-dataset evaluations. Furthermore, the regression framework demonstrates remarkable performance with a mean square error of 0.18$^{\circ}$C and an impressive $R^2$ score of 0.96. Our experiments' results highlight the developed system's effectiveness, positioning it as a promising solution for continuous temperature monitoring in real-world applications. With this paper, we release our dataset and programming code publicly.