We use both high-quality ear canal and anal thermometers, and while we have enough statistical grounds to unbias their results compared to each other, there remains significant variance. I.e. if we use an anal or ear canal thermometer makes temperature vary ±0.4 °C.

Then how sloppily you take the measurement with the same thermometer can result in a ±0.2 °C difference for the butt, and ±0.6 °C for the ear canal.

Of course, the time of day we take the temperature can give us a ±0.5 °C difference, and the activity level of the person something like a ±1 °C difference (we don't have as much data on these last ones, naturally.)

And all this is before you bring in the fever! So all of this we consider normal.

Basically, in our experience, anything below 38.4 °C could just as well be caused by any of a number of non-fever conditions at something like a 90 % confidence level, so unless there's a strong prior of fever, a "non-normal" temperature reading on its own is a fairly weak signal.

...which brings me to my final point: the prior ought to strongly affect what counts as normal temperature, but all of this discussion ignores it.

There's also the question whether you prefer false positives or false negatives when it comes to fever detection. My impression is that the medical community prefers false negatives, i.e. pretending that people with a low fever are perfectly normal -- but a lot of private persons I talk to have the opposite preference: they would prefer to think of someone as sick even though they are healthy.

Like any good medical test, you pick a threshold based on what probability you want for false positives and negatives, and you weigh the prior into this judgment. Just investigating what an average resting temperature with a particular measurement method seems to me silly.