Very true to what I remember as a child growing up 20 years later in the 80s. We would arrive at the waiting room, and I would immediately feel my face blush a little, as I was sure everyone there knew that I would be having something done in my bottom. After all, all kids got their temps taken in their bottom, as far as I knew, and I didn't seem to care as much that the other kids would be getting it, just that they all knew I would be.
Then, I was taken back to a small room with my mom, and instructed to get undressed to my underwear. It almost seemed silly to keep the underwear on, as they would be getting pulled down almost immediately when the nurse came in, and again at the end of the visit for the grand finale. The nurse would pop in and ask my mom a series of questions, including my temperature, and when and how it was last taken, which was of course answered "in the bottom". Then she would take my pulse and blood pressure, followed by the familiar "on your tummy so we can take your temperature". "Lift up for me....there we go" and my briefs would be down at my knees. Then she would turn and get the thermometer from a big jar, shake it down, and squeeze something from a tube on the tip, all while I was laying there bare butt at the ready. Then she would spread open my cheeks and slip the thermometer in, usually telling me "that's a good boy" and "just lay still for me". The thermometer would be very cold at first and uncomfortable, but then it would warm up and just feel "funny", with the weirdest feeling when it was pulled out. The nurse would wipe it and read it, and then tell me I could pull my undies up, and the doctor would be right in. At home, mom would always wipe me, but at the doctor's you were left with a slimy bottom.
After the exam, there was never a question, as I always got some kind of shot, whether a booster or penicillin. My mom would make me pull my underwear down so I would be ready when the nurse came in, which was very embarrassing for me, but the nurses always appreciated it. The cold alcohol would be swabbed on my bottom, then I would feel the pinch. I always cried up until age 8, when I started taking them better. Then I would be told how brave I was, etc., and be told I could get dressed. Once dressed I would walk out with a slimy, stinging bottom.
Very similar experiences growing up.