On peut la faire apparaître avant ça aussi, ce qui est plus le cas de Shin :
She spawns by a large stone pillar, between the shore of Quelaag's Domain and the waterwheel, in the swamp of Blighttown.
She will appear after having had your Pyromancy Flame upgraded to at least +10.(This wasn't necessary for me, she appeared even when I don't have a pyromancy flame, and with pyromancy flame at +0)
She may also appear simply if your Soul Level is sufficiently high (40-50; needs confirmation, but I encountered her on a pure strength build without a pyromancy flame at around this soul level)
She has been seen without carrying a Pyromancy flame at all, so the details to make her appear are uncertain. You do not need a Pyromancy of +10 or above in order for her to spawn. Whether or not defeating the Chaos Witch Queen is a requirement for her to spawn.
The Fire Tempest pyromancy will be available as a gift after fulfilling her request of defeating the Bed of Chaos. If you encounter the Bed of Chaos before finding Quelana, she will disappear.
Beating Quelaag is not a necessary requirement - she has spawned after a failed attempt on Quelaag's life, with a Pyromancy flame at under +10. Simply seeing Quelaag may be necessary (though it may not be sufficient in and of itself). (Confirmed, upgraded Flame to +10 before even going to Blighttown and caught a glance of her before getting into Quelaag's domain)
She can spawn without a Pyromancy Flame and without seeing Quelaag but by resons unknown (might be triggered by having enough inteligence)(I had her appear on my no-magic char because i had a friend co-op and he had pyromancy flame above 10+)
Looks like you have to rung the bell of awakening in the church first before she appears. (This is not necessary in NG+)