Febrile convulsions are worrying yes, I understand. But the risk of them is caused by a rapid rise in temperature, as opposed to the temperature itself. My niece is prone to them and rarely has high temperatures but just a rapid rise from 36 to 37.5 can cause her to fit. It's just the way she is.
If you can keep her cool in other ways, get air circulating, avoid covers and thick clothes etc, this helps to stabilise the temperature naturally. Offer lots of fluids when awake.
I would never tell somebody else not to medicate. That's what the medicines are there for. And you do what feels right for you and your dd and what makes her comfortable for the night.
A temperature is the body fighting off something and within reason I don't artificially lower it and trust dd's body to do its job. I of course give medicine if she is in pain or uncomfortable.
Keep an eye, you will anyway. Chances are it's a virus, but if anything changes, call NHS direct or OOH.
Oh and temp wise, you can use your body to see how she feels. Press your lips to her forehead and/or the back of her neck. You should be able to feel how hot she is from that. It's sometimes useful to get used to how she feels gauging her temp from your own body for those moments when you're worried about waking her/can't put your hand on the thermometer immediately. A well child just feels the same as you when you kiss their forehead/back of neck. If still running a fever, you can feel the heat on your lips.
Temp's always a bit higher at night too.