In some descriptions of God you might hear Him described as "the unmoved mover, the uncaused cause." If I properly understand the latter half of this statement, I can raise no objection. But I have heard the first half too often abused and misconstrued.
Many people say that God cannot be moved, He has no emotion, He is from eternity to eternity. I am not smart enough to argue with those people. But I think they miss something in the argument and in pure reason. Anyone who has any experience of life knows that it is not possible to love without being moved to action. Any love that is unmoved is not really love, but a vague shadow of it. Any parent who has loved a child knows that love means hurting, and longing, and hoping, and praying.
God longs for us. He loved us. He sent us an icon of His love--an icon that shows not the unmoved mover, but the deeply human Jesus Christ weeping--outside of a tomb, over the city of Jerusalem. This is not the unmoved mover. This is the engaged God, the God who loves us. The Icon of God is not the God who examines us with the microscope, but the Father who welcomes the prodigal, the Savior who weeps over our sin and death. Hardly unmoved.
As I recall, God is described by the theologians as attracting us as a magnet attracts iron (this is not the exact metaphor, but I don't recall the exact one), of moving us as a painting does by its beauty, etc. God's emotions toward us do not change; it is our experience of them (as changing beings) that changes, and which we misconstrue as change. But to perceive this as God's distant dispassion can also be wrong, since God is constantly active, and without his constant action everything would cease to exist.
No doubt I'm explaining this badly. Thomas Aquinas, for example, deals with this in the Summa Theologica.
We distinguish between unmoved and unmoving, between unchanging and static. God has no emotion, because emotion (as the theologians who say God has no emotion use the term) is a physical reaction, and God is spirit.
But yes, someone who's read the opening of St. Thomas's Summa Theologica once, and that recently, should probably not try to teach it to someone who hasn't read it.