I work quite a bit with thermal imagers, especially low-cost ones. In a drunken conversation earlier this week I talked with a few friends about the feasibility of doing exactly this.
You run into a bunch of challenges:
The first is that thermal imagers ("infrared cameras") don't directly measure temperature. By their nature they are estimating the temperature from the thermal brightness they detect. In the very best cases with high-end thermal imagers you might get an accuracy of +-0.8F. Lower-cost cameras more realistically have accuracies of around +-1.9F.
At the very best, you are measuring surface body temperature, not core temperature. So you need to deal with a lot of variables, such as local ambient temperature and humidity, subject body size, subject age, subject gender, Usually you will get the best estimates if you use the thermal brightness around the eyes (which are usually the brightest part of a face when viewed with a thermal imager. People's physiologies also vary enough that without a baseline you are unlikely to do very very well at estimating core temperature.
Your results will be best if the imager is very close (e.g. less than three feet) to the subject.
This excellent paper discusses some of the challenges in much more detail:
http://www.uhlen.at/thermology...
The upshot of all this is even if you did a very good job dealing with all of the myriad challenges and used a very expensive thermal imager you would unlikely to get an accuracy of much less then +-1.5F. In practice for something that would be commercially deployable at reasonable cost +-2.5F would probably be more realistic.
Those numbers aren't likely to be good enough to be useful in any practical sense. You might be able to use such a system to detect people with extremely high fevers, but such people are unlikely to be out and about walking around.
However, the approach of directly estimating temperature from a thermal image probably isn't the only way to crack this nut. Thermal imagers are extremely sensitive to small variations in temperature in their field of view (on the order of 0.02F -- you can easily image your bare footprints on a concrete floor for several minutes). My guess is that with appropriate sample data (you'd need thermal images of the faces of tens of thousands of people, many of them sick) you could use that relative temperature data to determine if someone had a fever or not.