Unlike several of Flame Breathing's other named forms, 炎天 required no interpretive leap from VIZ — it's a real, everyday Japanese compound for punishing summer heat, the same word in 炎天下の作業 ("working under the blazing sun"). Rengoku's technique borrows a weather word wholesale to describe a vertical arc of fire, which fits a broader pattern in this style: Flame Breathing's forms tend to be named for natural or atmospheric phenomena the flame resembles — a scorching sky, a swelling wave, an unrecognized fire — rather than for the cutting mechanics themselves, the way Water Breathing forms describe surfaces and currents ("water surface slash," for instance). "Rising Scorching Sun" needed almost no translator's liberty because the underlying Japanese was never technical jargon to begin with.
The corpus's raw OCR pass renders the Japanese callout for this form as "弐り型" rather than the correct 弐ノ型 — the katakana possessive marker ノ misread as the hiragana り. It's a small, forgivable slip, but a recurring one across this dictionary: technique names are lettered in a distinct display style set apart from ordinary dialogue, and that stylization consistently trips automated character recognition regardless of which breathing style or artist's hand is involved (see this hub's Beast Breathing entries for a more extreme version of the same problem).
Staging-wise, this form carries more narrative weight than its number suggests. It is the very first Flame Breathing technique the reader watches Rengoku land on-page in the Mugen Train fight — arriving one page after his self-introduction, "I AM THE FLAME HASHIRA KYOJURO RENGOKU" — even though his true combat debut in the volume, First Form: Unknowing Fire, technically happened earlier in the same arc against Enmu's puppet controlling the train itself. "Second Form" functions, for most readers, as the effective first impression of how Kyojuro Rengoku actually fights.