The wrath of God, like the hand of God, is an anthropomorphism - a poetic technique to describe the experience of God's absence (when it feels like God is mad at us, even though it is we who have left God).
God's wrath is, in otherwords, a direct extension of His love. In His love, He grants us free will that we may freely love Him, but He doesn't revoke that when we choose to reject Him through sin - instead, He allows us to know the consequences of our poor choices. Quite possibly, God could (and often does) withhold the full consequences, because He is patient and merciful; when we experience those consequences, it can feel like God is NOT being merciful (though He always does this in such a way as to call us back to Him) - hence we describe it as His wrath.
But it isn't as if God's emotions change - as though He had emotions like humans do, or wrath like humans do. God is love. That never changes; we change, though, so sometimes we experience that love as wrath (think like how a child sometimes experiences the discipline of their parents as "wrath" even though it is honestly and truly an act of love on the part of the parent).
Hope that helps.
In Christ,
Macarius