Massive and unobtrusive screening of people in public environments is becoming a critical task to guarantee safety in congested shared spaces, as well as to support early non-invasive diagnosis and response to disease outbreaks. Among various sensors and Internet of Things (IoT) technologies, thermal vision systems, based on low-cost infrared (IR) array sensors, allow to track thermal signatures induced by moving people. Unlike contact tracing applications that exploit short-range communications, IR-based sensing systems are passive, as they do not need the cooperation of the subject(s) and do not pose a threat to user privacy. The paper develops a signal processing framework that enables the joint analysis of subject mobility while automating the temperature screening process. The system consists of IR-based sensors that monitor both subject motions and health status through temperature measurements. Sensors are networked via wireless IoT tools and are deployed according to different configurations (wall- or ceiling-mounted setups). The system targets the joint passive localization of subjects by tracking their mutual distance and direction of arrival, in addition to the detection of anomalous body temperatures for subjects close to the IR sensors. Focusing on Bayesian methods, the paper also addresses best practices and relevant implementation challenges using on field measurements. The proposed framework is privacy-neutral, it can be employed in public and private services for healthcare, smart living and shared spaces scenarios without any privacy concerns. Different configurations are also considered targeting both industrial, smart space and living environments.