Although the Vidyashankara temple is commonly assigned to the14th century, Amita Kanekar’s architectural study shows that such an early date is inconsistent with its design which clearly points to a later period.

The temple’s core structure is firmly in the Dravida (Tamil) style, with pillars and hall elements characteristic of the Keladi Nayaka and Vijayanagara tradition of the 16th century. However, the Hoysala-looking exterior is a conscious archaic revival, not an actual work of the Hoysala-era. There is no Bijapur Sultanate influence in its construction.

All these would confirm that the Vidya shankara temple at Tunga Sringeri was erected before the post-1565 rise of Bijapur architecture.Therefore, the 14th century dating is incorrect.

According to Kanekar, the temple was almost certainly built under the Keladi (Ikkeri) Nayakas in the 1500s.

for further study:

https://easaa.org/wp-content/uploads/2023/01/Amita-Kanekar-5.pdf