The respiratory viral diseases, such as those caused by the family of coronaviruses, can be extremely contagious and spread through saliva droplets generated by coughing, sneezing, or breathing. In humans, the most common symptoms of the infection include fever and difficulty in breathing. In order to reduce the diffusion of the current "Coronavirus disease 2019 (COVID-19)" pandemic, the Internet of Things (IoT) technologies can play an important role; for instance, they can be effectively used for implementing a real-time patient tracking and warning system at a city scale. Crucial places to install the tracking IoT devices are the public/private vehicles that, augmented with multiple connectivity solutions, can implement the Internet of Vehicles (IoV) paradigm. In such a ubiquitous network environment, vehicles are equipped with a variety of sensors, including regular cameras that can be replaced with thermal cameras. Therefore, this paper proposes a new design for widely detecting respiratory viral diseases that leverages IoV to collect real-time body temperature and breathing rate measurements of pedestrians. This information can be used to recognize geographic areas affected by possible COVID-19 cases and to implement proactive preventive strategies that would further limit the spread of the disease.