"Angelkisses " it is certainly a question of age
I presume that you are still rather young because at least in France in the 50's as a child and a small kid under 12, I had always my temperature taken rectally, it was considered by doctors and nurses as more accurate than the oral temperature.
I have been told that it was the same in hospitals and clinics at that time even if I have not not experienced it myself
Even at school, the middle aged permanent nurse performed always a rectal temperature at middle schoool and sometimes even at high school in the first 60's if she suspected a boy student to be a liar about his sickness to escape to a PE lesson, it was a kind of thread to dissuade the students to lie, the surprise was great the first time for a teenager boy when he was instructed by the nurse to remove his clothes including his brief and to lie on his belly on a medical table where she would come to insert the thermotheter in his naked anus while she put her other hand on one of his cheek, and she took her time to make it more embarrassing, so it was enough efficient.
It happened to me two or three times at middle school and one in high school when I was a freshman, ( and the last time the permanent nurse was assisted by a student nurse who was at school for a training course and was still young and as she explained her how to proceed, how to touch me and so on ...,it took still more time and it was still more embarrassing to stay with my naked butts exposed for a more long while under their sight, so I understood that I might not lie...)
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I don't know if she did it also with an older teenager of 16 or 17 age but I think so.
I believe that it was depending also of his more or less suspicion towards the boy student and may be also if she was in a bad mood or a good mood because one time she had not taken my temperature.
At least our PE teacher told it to us as a thread at the beginning of the year school during the first lesson and it was the rumor which spread all the time in locker rooms and corridors and break time in the playground of the school that even a 17 age student could have his temperature taken rectally if he was unfortunate. It was related also that a boy student who came to the nurse office and seemed to her too arrogant could be submitted to a rectal temperature as a kind of punishment. May be a legend but may be not, how to know...
Normally at home, we were told also to continue to take our temperature rectally but in most families we could do it ourself in privacy even if it could be depending on families.
As regards the inspection of the penis and palpation of the balls and rolling them between fingers, it was quite a standard procedure at school examination but seldomly performed by private doctor. I had not a pediatrician but a regular doctor, I believe that on the rreverse of today, there was a very few number of pediatrician doctors at that time while now almost all families who have children send them to see a pediatrician.
Like every doctor knew that we had an annual mandatory school exam, they thought that except in specific cases, it was useless to perform a check of the genitals. If a check was decided , for instance for me by a doctor at 15 age, he pulled down himself my brief until knees and when he had finished, he instructed to me after to slip of it and to turn around for a check of the curvatures of the spin and then to move forward and down a few steps in the examination and eventually to move to the wall and to stay here face to the wall before bending over . It was in presence of my mother but fortunately she looked away at that while of the examination.
As regards the visual inspection of the anus, it was not a common practice in my knowledge except of course if you had rashes or other issues in that part of the body.
My first digital rectal examination took place as a draft at a pre-induction medical center for military service and was performed by a male military service, never at school or university.
At that time it was considered that a DRE was not necessary for boys according to most of doctors because a testicular cancer was very very seldom for a kid or a teenager, but of course a very cautious doctor who knows that it can nevertheless occur would do it, and now I think that it is him who is right if there is even a small risk...