I would have thought most children would have been poorly enough to warrant some medication before they reach 15 months, although I'm sure like everything that there are some who don't. I guess they are lucky. But then I've always given mine something when they seem to be suffering rather than going by temp, so that has meant occasionally giving them something when teething so definitely before 15 months.
I don't think I give it too readily, DS(3) was recently admitted to hospital with breathing difficulties (due to a virus), but because despite struggling to breathe he seemed to be perfectly happy (kept insisting to the Drs that he was fine), I hadn't dosed him. When we were in the hospital they took his temp, decided it was high, and they did give him some calpol and told me to keep him dosed up while he was unwell.
I'm another that would never know that dc were running a temp without them acting unwell though, so I wouldn't give medicine for that alone. IME when they have had a high temp, 39 or above, they have been very unwell though.
Interesting about the speed the temperature goes up. I always thought it was a risk when temps were over 39 or so in small children.