The key is understanding the difference between Umbral Ice and Umbral Fire. Although the base Fire/Blizzard spells have equivalent potencies, Umbral Fire will increase the damage of successive fire spells beyond that base amount (while also increasing their mana cost). As such, in terms of sheer damage per second, Fire is far more effective. However, as Umbral Fire simultaneously increases the cost of your Fire spells, continuous casting will empty out your mana pool. At that point, you want to leverage Umbral Ice to quickly restore your mana. Early on, this is achieved with Transpose; later on, with Blizzard/Fire III.

Thunder has a small initial kick and a DoT. As such, the longer it's active, the more damage it does. As a DoT, it ticks without any effort from you, and so once cast, will increase your damage per second without any additional effort on your part.

Long story short, you want to open with Thunder, then go with Fire until your mana is almost drained, hit Transpose, and depending on mana/timing, probably Thunder again and resume Fire with maybe a Blizzard in the middle, if necessary. It's really important as a THM/BLM to have a feel for how your mana will regen and balance your DPS accordingly.
Also, Scathe - as an instant cast spell - is often very useful as a finisher, i.e. follow up your last Fire/Blizzard with it, when the mob is almost dead, for a quick end to the battle.