The fifteen gods of Theros are a diverse bunch, and since we've only gotten to know the five principal ones so far, there's plenty to speculate about with regard to their two-color counterparts. The enemy-color gods, who include Iroas, will apparently be appearing in no particular order in Born of the Gods and Journey into Nyx, and they count an even more enigmatic figure than the former among their number. That individual is Kruphix, the green and blue god of (apparently) time.
Kruphix may share a color combination with Ravnica's Simic Combine guild, but in flavor, mechanics, and personality he seems quite distant from that organization. Whereas the Simic are about using blue's manipulative and shapeshifting magic upon green's purview of nature, Kruphix and his followers seem to use green's belief in destiny and harmony to craft blue's temporal magic. He doesn't seem to be based on any one Olympian god in particular, but the flavor text of Agent of Horizons, one of his worshippers, appears to imply that he's at least somewhat influenced by Hermes. But his major source material seems to be the more obscure non-Olympian gods - the barely-personified primordial entities like Phanes and Ananke that represent circularity and inevitability.
The best source we have for the possible mechanics and personality of Kruphix is, well, Prophet of Kruphix. The flavor text - "Time is fluid as a dance, and truth as fleeting." - clues us into the fact that Kruphix is, indeed, probably the god of time.
He's worshiped at the Temple of Mystery, whose art description, recently posted in the Temple of Mystery Arcana article on the mothership, refers to him as the "god of horizons":
The Greeks believed that there was an end to the world where the sea drained off a sharp edge and formed an epic waterfall. The camera is facing this epic waterfall. At the top of the waterfall, there is a massive tree growing up out of the water. We can see water cascading down over its roots and into the abyss below. This tree is a shrine to the enigmatic god of horizons. The tree should be a fantastical version of an olive tree.
However, this is probably a poetic descriptor and not literally what his divine province is.
He seems to be quite neutral among the other gods, probably believing himself above petty feuds such as Purphoros's unrequited love for Nylea and Iroas and Mogis's sibling hatred.