The answer to the question: What is the full name of the temple built in the style that shows distinct Dravidian influences in 1279? is inside the article: The modern interest in the Hoysalas is due to their patronage of art and architecture rather than their military conquests. The brisk temple building throughout the kingdom was accomplished despite constant threats from the Pandyas to the south and the Seunas Yadavas to the north. Their architectural style, an offshoot of the Western Chalukya style, shows distinct Dravidian influences. The Hoysala architecture style is described as Karnata Dravida as distinguished from the traditional Dravida, and is considered an independent architectural tradition with many unique features.A feature of Hoysala temple architecture is its attention to exquisite detail and skilled craftsmanship. The tower over the temple shrine  (vimana) is delicately finished with intricate carvings, showing attention to the ornate and elaborately detailed rather than to a tower form and height. The stellate design of the base of the shrine with its rhythmic projections and recesses is carried through the tower in an orderly succession of decorated tiers. Hoysala temple sculpture replicates this emphasis on delicacy and craftsmanship in its focus on depicting feminine beauty, grace and physique. The Hoysala artists achieved this with the use of Soapstone (Chloritic schist), a soft stone as basic building and sculptural material.The Chennakesava Temple at Belur (1117), the Hoysaleswara temple at Halebidu (1121), the Chennakesava Temple at Somanathapura (1279), the temples at Arasikere (1220), Amruthapura (1196), Belavadi (1200), Nuggehalli (1246), Hosaholalu (1250), Aralaguppe (1250), Korvangla (1173), Haranhalli (1235), Mosale and Basaralu (1234)  are some of the notable examples of Hoysala art. While the temples at Belur and Halebidu are the best known because of the beauty of their sculptures, the Hoysala art finds more complete expression in the smaller and lesser known temples. The outer walls of all these temples contain an intricate array of stone sculptures and horizontal friezes (decorative mouldings) that depict the Hindu epics...., can you guess it ?
The answer to this question is:
Chennakesava Temple at Somanathapura