Concept:
The Sun Temple at Konark is a masterpiece of Indian architecture and a UNESCO World Heritage site. To answer this, one must be familiar with the timeline of the Eastern Ganga Dynasty and the reign of King Narasimhadeva I.
Step 1: Historical Context and Patronage.
The temple was commissioned by King Narasimhadeva I of the Eastern Ganga Dynasty. Historical records and architectural evidence place the construction during his reign. The specific period is:
$1238 - 1264$ CE
Step 2: Converting the Year to Century.
In history, the "century" is always one unit ahead of the starting digits of the year. Since the temple was built in the mid-1200s:
$1250 \text{ CE} \rightarrow 13\text{th Century}$
This period marks the height of Kalinga architecture, characterized by the temple's massive chariot shape with 24 wheels and 7 horses, all carved from stone.
Step 3: Architectural Significance.
The temple is also known as the "Black Pagoda" due to its dark color and was used as a navigational landmark by sailors in the Bay of Bengal. The precision of the carvings and the alignment with the sun's rays demonstrate the advanced scientific knowledge of the 13th-century engineers.
Final Answer: Option C