I believe God is impassible, though I don't believe Divine impassibility means God is some kind of "divine stoic". Rather, God is without the fickleness, mutability, and pettiness that is inherent to our human, particularly our fallen human, emotions.
St. Ignatius in his Christological hymn speaks of Christ as both passible and impassible, as regards His humanity and Divinity.
Impassibility, to me, points to God's immoveable nature; it means that God is non-reactive. He loves us, for example, because that is Who and What He is; it is not a response toward our doing something or saying something that He then reacts to favorably. Likewise, when we speak of God's wrath, it would be wrong to think of this in terms of reaction--as though we hurt God's feelings and now He's mad at us, or wants to "get back" at us.
God loves us because that's God being Himself, and we can't make Him love us or make Him stop loving us--it's Who and What He is. God's wrath is not God being mean, cruel, or "angry" in the sense of the ways we get angry when we are hurt and take action against another; but rather wrath is what we behold when we see God through the lens of His Law in the guilt and brokenness of our own sin. When I look at God hidden in His divine majesty and holiness, when I look at the Law, I see that I have fallen short, immeasurably short, incomprehensibly short, and that I am indeed a sinner and a wretch. But God Himself, in His disposition toward me as He reveals Himself in Christ, is the God who descends into weakness, humility, suffering, and death in order to rescue me.
So the Law is a mirror and what I see is terrifying, because I see myself as the naked wretch that I am before a truly good God; but God toward me is the love and grace super-abundantly poured out through the life, suffering, death, and resurrection of Jesus Christ.
In the Law I see that I am sinful beyond measure; in the Gospel I find that God is loving and compassionate beyond measure. And the meeting place of these two things is the Cross of Jesus, who bears the entirety of the weight of my sin and death, and reconciles me to the Father by way of Himself, and gives me the Holy Spirit by whom I a may now call out to the Father, "Abba! Father!". So great, so immense, so amazing the loving kindness of God.
-CryptoLutheran