@Jacana "One wonders why they would inflict something so undignified. I'm sure that if at age 14 you can deal with tampons and periods you can deal with a thermometer up your anus on your own."
"I too had appendectomy, and the policy also was to take rectal temperatures. Like yourself, I was to roll on my side and lower my pajamas (or whatever I was wearing). The difference is that I would do it under bedsheets: the nurse handed me the thermometer and I would insert the tip into my rectum. I was expected to know how to do this at that age, given that it was a very common way of taking temperatures in French households. Indeed, in my home this is how it went if I was sick (of course when younger mom would do the honors)."
A few thoughts come to mind as to why they didn't have the patient insert the thermometer themselves. From what you've said, rectal temps were routinely taken, regardless of age. So a 14 year old would have known how to do that. But in the USA, rectal temps ended much younger. From what I've read here and elsewhere, some stopped at four or five; mine stopped around ten, and apparently some went beyond that. For those who stopped at 5, they may not have known how to take the temperature rectally. Which leads to the second possibility. My understanding is the European analogue thermometer has always been the same as the ones currently used, with a narrow tip and then a broad shoulder. Only the tip is inserted in the anus and there is no need of lube. Prior to the Geratherm non-mercury thermometers, thermometers used in the USA were slender and the same thickness the whole length. They were inserted a couple inches into the rectum, and therefore required lube. Making sure the kid inserted the lubed thermometer properly might not have been so straight forward. Also, if you're taking temps on a ward, it's done mass production style. They're probably not going to individually assess each patient for their ability to insert the thermometer. The other issue, which I think was prevalent throughout medical care, at all ages, is embarrassment isn't a reason to not do something which is helpful.
That said, I think there is a place for considering the patient's feelings, although back then that wasn't the case.
Certainly when boys had sports physicals at school and a female teacher or other staff member was there when they had to drop their shorts, no one cared how the boys felt about it. And they weren't even medical personnel.