Does god have a mind? If yes, it is an exception for God that body and mind are temporary, only Atma /Brahman is the permanent?
The answer can depend upon what Vedanta philosophy you adhere to. According to the Advaita, mind is one of the kosas. See here - Where does a Soul attach to the Body? and here - Where does the four states of consciousness occurs in an individual?. Mind is a state of perceptual consciousness shared by by living beings and man. Brahman has no mind - what is there for Brahman to think about? What is there for Brahman to understand? Brahman knows all, past, present, and future. Brahman is beyond mind. Brahman is Pure Consciousness. Iswara - Saguna Brahman - is how we perceive Brahman, because we, with our limited mind and senses, cannot comprehend the true nature of Brahman. We make an anthropic vision of Saguna Brahman.