Fire IV is enabled by Enochian. Enochian, once activated, will last as long as you don't let Astral Fire / Umbral Ice fall off. It doesn't matter what tier of element buff you keep up for this purpose -- Transpose is enough to keep Enochian active forever.
At Lv60, the basic basic rotation without extra cooldowns looks something like this:
Blizzard III (enters Umbral Ice)
Enochian
Thunder III
Blizzard IV (grants three Umbral Hearts*)
Fire III (switches to Astral Fire)
Fire IV (2 hearts remain)
Fire IV (1 heart remains)
Fire IV (0 hearts)
Fire (refreshes Astral Fire)
Fire IV
Fire IV
Fire IV
Repeat from Blizzard III, skip Enochian because it will still be up as long as you haven't let your Fire/Ice buff fall off.
* Umbral Hearts: normally, Fire spells cost double when you are in Astral Fire. Umbral Hearts waive the doubling. The Fire III after Blizzard IV doesn't cost any extra because you're not in Astral Fire yet. The first three fire spells after that will cost the base cost. The fourth fire spell through the last will cost double.
It's useful to note that Fire and Fire IV cost the same, so if your spell speed isn't high enough for IV-IV-IV-I, you can do IV-IV-I-IV and it won't cost any extra for shuffling the 1s and 4s around. But you want to aim for higher spell speed so you can do IV-IV-IV- I -IV-IV-IV - BlizzardIII.