Did God change from a wrathful God to a loving God between Old Testament and New Testament? This question is mainly to the evangelical Christians and Bible believing Christians, who believe that God doesn't change and His nature is Love.
The Old Testament is filled with accounts that describe how God poured out His wrath on people, including His chosen people, the Israelites. However, when we read the New Testament particularly the life, teachings and message of the Lord Jesus Christ we don't see the outpouring of God's wrath on people. Instead, we read about God's grace, mercy, and love. How do we square these two seemingly opposite manifestations of God's nature?
There was a gap of about 400 years between the two Testaments, with the OT covering a vast time span, from creation till then.  Taking the time from after the Flood, that alone has been variously calculated as 2,454 years to 2,518 years.  This means that the OT deals with about two and a half thousand years of history after the Flood, whereas the NT only covers less than seventy-five years of history! The NT does not detail the horrific destruction of Jerusalem and its temple in A.D. 70 as all but its last book was completed before then. (The last book named Revelation may have used coded language to infer that event but it deals a lot with future events where the wrath of God will be poured out on the nations.)
It is unbalanced to compare the historical dealings of God with his people and the nations over thousands of years, with a mere 75 years history in the NT. This is especially so when the NT does not hold back from warnings about the coming wrath of God, both on individuals who continue in rebellion against him, and the various “bowls of wrath” coming on the whole world before Christ returns in judgment.
The idea that God must have changed in nature between the two testaments may indicate some ignorance of what those two testaments state, on the matter of God’s nature and his dealings with mankind. In both testaments, the immense patience and love of God is demonstrated, yet without holding back from clear evidence of God’s holiness, righteousness and sovereign judgements. There may be a bit of ‘cherry-picking’ going on, selecting gruesome events in the OT (which tells things the way they were) while only citing nice sentiments expressed in the NT.
Finally, you addressed your question to evangelical, Bible believing Christians, “who believe that God doesn't change and His nature is Love.” As one such Christian I would point out that the Bible does not limit God’s nature to love, but that his love is perfectly balanced with his holiness, his righteousness and his justice. It’s imbalanced to focus only on God’s love, as if a loving God would sweep sin under the carpet without judging sin and sinners. In his love, God has done everything we could never do to spare repentant sinners the punishment due their sin, by pouring it out on the sinless Son of God instead. But if people disregard what God has lovingly done, they will have to bear that punishment. Then they will know the righteous wrath of God. That was the pattern in the OT because forgiveness and time to repent was always available to those seeking to please God, and that continues in the NT. No change there, God be praised!