I don't think there is any claim that the same instrumentation is used for the Union Army cohort -- even basic details like whether the temperature is taken orally or axially: "Whether the temperatures were taken orally or in the axilla is unknown; both methods were employed in the 19th century although oral temperature was more common".
That's true, but they do make the more abstract assumption that any bias isn't associated with birth date within cohort. I think the idea is that if there were bias due to instrumentation, it would have to be somehow systematically related to birth date within the cohort.
This is possible if there were some systematic shift in instrumentation with measurement year, but it would be blunted by the extent to which different ages were being sampled at each year.
I agree though that it would be nice to have some information on instrumentation over time and how it relates to temperature measurement.
It's worth noting that the results have practical implications regardless of the explanation of the observed trends, though, which is it's commonly assumed normal body temperature has certain characteristics, without recognizing that that might have shifted in significant ways over time.
It's interesting to me personally because I've often observed my body temp when I'm feeling fine is usually just above 36 C. That doesn't sound like much but it becomes a bigger deal when deciding whether or not I have a significant fever. Some of that might just be individual variation, but this is suggesting there's cohort trends within that too.
