I'm hoping this will help you... I have medium thick hair (density) and my strands are medium (just a little smaller than a strand of thread), and if I go by the hair-typing system, my hair looks like it is probably 3c in the very front (bangs), the nape, and behind my left ear (weird right?), but the rest seems to look like it's 4a.
In June a stylist KILLED my curls in the front when she flat ironed my hair on 450 with two passes. My hair looked amazing after she straightened it, but now my hair does not curl at all in the front, the nape or behind my left ear.
On Sunday I decided to flat iron on my own to trim it, and I used the recommended heat setting on the box for medium textured hair, (250) and my hair looked great, and it curled back up immediately when I washed it out.
Since you have fine strands, perhaps trying 200 and moving up will be a good idea...I'm hoping your FI has temperature settings.
HTH!