Although rectal temps in our household growing up were common place, they were really quite private. Sometimes other adults might see them to us, but I can only remember three times seeing them happen.
My youngest sister, I remember seeing mom take her temperature on the diaper table in the diaper position. I would say she was less than a one and my sister did have BM while this was being done.
The second time was my middle brother and I arrived in the kitchen from playing outside and my mom was taking his temperature over the knee. His pants and undershorts to the ankles. I remember him saying get out. My mothers friend who was there with her escorted me from the kitchen. My brother got spanked after the rectal temp for not cooperating I guess. I did hear the spanking and him crying.
And the last one was my youngest brother. It was done by Aunt who was a nurse. She came over and my mother brought my brother into her bedroom and my aunt took his pants and shorts down put him over the knee and lubed the thermometer with Vaseline and took it. He complained some but she was firm with him. I was outside the bedroom but could see it all.
As I said it was quite private. In my case, I remember in the second grade I was home sick for a week from school and I guess I was not contagious cause my mom let a few a mom friends visit me with school work. The rectal thermometer was on the night table with the Vaseline next to my bed and after a few minutes she told them had to leave because she needed to take my temperature. The all smiled and left.
In my adult life, my wife who has since passed away had her temperature taken rectally at the hospital in the ER. She had cancer and was nauseous from the chemo and took it rectally with me present. It was the probe type and they just took her slacks down and panties down and rolled her on her side to do it.