Please see Part 1 of this article for more on the natural history and care of Rough and Smooth Green Snakes (Opheodrys aestivus and O. vernalis).
An ambient temperature of 70-76 F is ideal. A basking site of 80-85F should be available as well.
There is some evidence that, in contrast to most snakes, Green Snakes benefit from exposure to UVB light. A moderate-output bulb, such as the Zoo Med 2.0 should be provided.