NOTE: I assume, in this post, that God is the protagonist of the Bible: God is the main character throughout Scripture.
Yahweh, the personal god of Israel who is actually God of the universe, is repsonsible for the exile of Israel. He uses proxies (kings of Assyria and Babylon), but He is the one ultimately responsible. He displays his wrath by subjecting Israel to military defeat, opening their eyes to the outcome of their sin. He sends them into exile so that He can bring them back with greater maturity and less proneness to sin. This is the point of punishment. However, by using proxies, Yahweh subjects himself to the ridicule of the proxy. In a culture where military conquests display the superiority of your gods to the nation you just defeated, a defeated Israel means a humbled Yahweh: In the eyes of all surrounding nations, especially the nation that just defeated Israel, Yahweh is unable to protect Israel and is therefore weak.
Of course, Yahweh knows better and Israel's prophets know better, but they are the only ones. In punishing his own people, Yahweh is humiliating himself in the eyes of the seeing world. In sum, when Yahweh punishes Israel, Yahweh subjects himself to ridicule, mockery, and scorn. Yahweh's wrath cannot be displayed in a henotheistic (look it up) context without necessarily showing his humility. Basically, Yahweh is willing to show His wrath so that Israel will not remain stuck in the cycle of sin. Israel's long term good supercedes His short-term honour. That sounds alot like sacrificial love, to me: Yahweh is sacrificing His honour for the good of His people.
Fastforward to Jesus. Jesus puts himself in the story of Israel and even suffers the consequence he predicts for them: He suffers as a failed militant Messiah even though he is not a military threat. On his way to the cross, he even tells Israel not to weep for him, because if they continue on their path, they will suffer a worse fate (Luke 23:27-31). He accepts the coming display of Israel's final exile: The rout at the hands of the Romans that comes in A.D. 70. If this is a form of exile, then God is responsible. God's wrath is vented on Israel so that they will abandon their misguided attempts at being His people. But even before this, God humbles himself and accepts the future outcome of his wrath by subjecting himself to the cross. Again, the sacrificial love of God is shown: For the long term good of his people (though in Israel's case it is rejected and they do suffer his wrath in A.D. 70 and again in 135), God suffers the humiliation of the cross.
If all the above works out, I think that humility is the connecting factor between the wrath and love of God.