I'm currently visiting India, and I just went to the Ulagalantha Perumal Vamana temple in Thirukoilur. It's most famous for being the "Naalayira Divya Prabandha Avatara Sthalam", meaning the birthplace of the poems of the Alwars. That's because Thirukoilur is the place where, as I discuss in this answer, the first three Alwars saw Vishnu in the cave. It is also one of three temples that claim to be the place where Vishnu's incarnation Vamana defeated Mahabali, which is why the main statue of the temple depicts Vamana taking his three steps of land:
Now Thirukoilur is one of the 108 Divya Desams, the sacred places of Vishnu praised by the Alwars. But I learned from the priest that it's more than that: he said it's one of the Pancha Krishnaranya Kshetras, the five Divya Desams where the deity of the temple is an incarnation of Krishna, rather than just being an incarnation of Vishnu. So my question is, is it true that the Vamana deity in Thirukoilur is an incarnation of Krishna?
And if it is true, what exactly does it mean? Does it mean that Vamana himself was an incarnation of Krishna? Or does it mean that the Vamana statue in this temple was a manifestation of Krishna? Or does it mean that it was Krishna who appeared before the first three Alwars? The latter is a possibility because the Alwars are said to have been born in the Dwapara Yuga, as I discuss in my question here.
By the way, this Wikipedia article says that the Pancha Krishnanaranya Kshetras have nothing to do with Krishna other than having an Utsavar or processional idol of Krishna.
Krishna is not the presiding deity in any of the temples. The processional deity, Krishna, led to the derivation of the names of these places. There are five similar temples located in North India, called Pancha-dvarakas.
But I'm not sure whether that's accurate.