In classic the god would be the god of that temple, but here it's chosen at random. UESP states:
c0b20y08"They tell me that you quite loyal to the temple. I need you perform a vital task for us. (Temple's god) has become angry with us. You need not concern yourself with why. Our only hope is to hold a rite of atonement. We need (ingredient) for the ceremony. My sources tell me that some can be found in (dungeon). Will you bring it to us?"