The answer differs depending on which religion/sect/philosophy you adhere to, but God is usually attributed some sort of emotion, or at least a will, because without it the belief in God can’t serve a societal use.
Say you assume a God without emotions. From this it results that nothing we may do or fail to do would impact them, so there are no sins, no divine laws, prayers and rites are useless… So your belief can’t be a religion; nor can it be used to control people. There’s no physical use to preaching belief in God, and not much of a metaphysical need either since God doesn’t care whether you believe in them. “God” becomes a concept like the laws of physics, there’s not even much meaning in considering it as a being. There’s little difference between an emotionless God and no God at all. So all religions will personify God to some extent.
Calvinism still has a notion of divine will, even if there’s no divine judgement. Maybe the notion of “will” can be dissociated from the notion of “feeling”, but that’d be a debate in itself, I personally tend to think that it can’t: Awareness can only indicate what is, not what should be.
As for all the religions with an intermediate between God and men, either they represent God’s will… In which case, God does have a will; either they have their own will. And this just displaces the question, because if God has no will but his angels do, then the angels are effectively the Gods: They’re the ones whose favour prayers are supposed to get.
Also, when I mention the “societal use” of a religion, what I mean isn’t how the religion is useful to the believer, but how it makes the believer useful to the state and/or clergy. My point was that religion with a personalized God who directly judge human actions tend to dominate because they’re most useful as tools to influence people’s actions.