"He who believes in the Son has everlasting life; and he who does not believe the Son shall not see life, but the wrath of God abides on him.”-John 3:36
I don't think it's safe to say that that verse applies only to Old Testament times? Nowhere in God's Word are we told that God changes His attituded toward unrepentant sinners. The cross shows how serious God takes sin. He does not punish the sin but the sinner in hell if he does not repent and trust in Christ.
There are so many New Testament verses that warn about God's wrath.
Jesus said, “And I say to you, My friends, do not be afraid of those who kill the body, and after that have no more that they can do. 5 But I will show you whom you should fear: Fear Him who, after He has killed, has power to cast into hell; yes, I say to you, fear Him!-Luke 12:4-5
"26 For if we sin willfully after we have received the knowledge of the truth, there no longer remains a sacrifice for sins, 27 but a certain fearful expectation of judgment, and fiery indignation which will devour the adversaries. 28 Anyone who has rejected Moses’ law dies without mercy on the testimony of two or three witnesses. 29 Of how much worse punishment, do you suppose, will he be thought worthy who has trampled the Son of God underfoot, counted the blood of the covenant by which he was sanctified a common thing, and insulted the Spirit of grace? 30 For we know Him who said, “Vengeance is Mine, I will repay,” says the Lord. And again, “The Lord will judge His people.” 31 It is a fearful thing to fall into the hands of the living God."-Hebrews 10:26-31
"6 Then I saw another angel flying in the midst of heaven, having the everlasting gospel to preach to those who dwell on the earth—to every nation, tribe, tongue, and people— 7 saying with a loud voice, “Fear God and give glory to Him, for the hour of His judgment has come; and worship Him who made heaven and earth, the sea and springs of water.”-Rev.14:6-7
“The fear of the LORD is the beginning of wisdom, And the knowledge of the Holy One is understanding."-Prov.9:10
"In mercy and truth Atonement is provided for iniquity; And by the fear of the LORD one departs from evil."-Prov.16:6
Edit: included the scripture reference(John 3:36) after first verse posted.