Depicting the Tempter

There's a conventional interpretation of Gen 3 which visualizes the Tempter as a bipedal reptile that's able to communicate with Eve due to Satanic possession. I'm curious about the historical origins of that tradition.

In my limited knowledge, early artistic representations of the Tempter depict a zoological snake (e.g. Trinity sarcophagus, sarcophagus of Junius Bassus) while later artistic representations depict the Tempter as a hybrid creature: a human-headed snake (e.g. Ghiberti, Mantegna, Masolino, Michaelangelo, Holbein the Younger)–although later artists sometimes continue to depict the Tempter as a zoological snake (e.g. Cranach). 

In Milton, the Tempter is a fallen angel who's cursed to become a snake, after the Fall. Hugo van der Goes depicts the Tempter as a human-headed lizard, standing on its hindlegs, leaning on the tree of knowledge. 

In none of these examples is the Tempter a Satanically possessed bipedal reptile that became a snake after the Fall. So I wonder when that exegetical tradition developed.