The biggest challenge with how easily SARS-CoV-2 spreads is that pre-symptomatic people are perhaps the most likely to infect others. Some studies suggest that people shed the most virus in the two days leading up to symptoms. So taking temperatures, convincing people to stay home when sick, only goes so far. That’s why healthy people are asked to wear masks, because they may be infecting others without realizing it.
Another big problem though is that even people who test positive for the virus aren’t staying home. Some are hiding their diagnosis, and still traveling.