A cursory reading of the Bible -- the punishments in the Old Testament vs. Jesus' miracles and forgiveness of sins in the New Testament -- can lead one to the conclusion that God is full of wrath in the Old Testament yet has seemingly changed to become more loving in the New Testament. A more careful examination indicates that God is loving, merciful, and full of wrath toward unrepentant sinners (because He is just) in both the Old and New Testaments.
Consider how God describes Himself to Moses on Mount Sinai:
The Lord descended in the cloud and stood with him there, and proclaimed the name of the Lord. The Lord passed before him and proclaimed, "The Lord, the Lord, a God merciful and gracious, slow to anger, and abounding in steadfast love and faithfulness, keeping steadfast love for thousands, forgiving iniquity and transgression and sin, but who will by no means clear the guilty, visiting the iniquity of the fathers on the children and the children's children, to the third and the fourth generation."
The wrathful and (supposedly) unloving God of the Old Testament leads His description of Himself as loving, merciful, and forgiving. It is only at the end of His description that He warns that He will punish the guilty (as His Justice demands).
The Old Testament has a recurring theme of God bestowing His Love upon humans as a bridegroom upon his bride only to be rejected by humans disobeying Him, committing horrible sins (murder, rape, child sacrifice, etc.), and "whoring" after idols like an adulterous wife. Consider some of what God said to Ezekiel about the Israelites ("Jerusalem"):
I made you flourish like a plant of the field. And you grew up and became tall and arrived at full adornment. Your breasts were formed, and your hair had grown; yet you were naked and bare.
"When I passed by you again and saw you, behold, you were at the age for love, and I spread the corner of my garment over you and covered your nakedness; I made my vow to you and entered into a covenant with you, declares the Lord God, and you became mine. Then I bathed you with water and washed off your blood from you and anointed you with oil. I clothed you also with embroidered cloth and shod you with fine leather. I wrapped you in fine linen and covered you with silk. And I adorned you with ornaments and put bracelets on your wrists and a chain on your neck. And I put a ring on your nose and earrings in your ears and a beautiful crown on your head. Thus you were adorned with gold and silver, and your clothing was of fine linen and silk and embroidered cloth. You ate fine flour and honey and oil. You grew exceedingly beautiful and advanced to royalty. And your renown went forth among the nations because of your beauty, for it was perfect through the splendor that I had bestowed on you, declares the Lord God.
"But you trusted in your beauty and played the whore because of your renown and lavished your whorings on any passerby; your beauty became his. You took some of your garments and made for yourself colorful shrines, and on them played the whore. The like has never been, nor ever shall be. You also took your beautiful jewels of my gold and of my silver, which I had given you, and made for yourself images of men, and with them played the whore. And you took your embroidered garments to cover them, and set my oil and my incense before them. Also my bread that I gave you -- I fed you with fine flour and oil and honey -- you set before them for a pleasing aroma; and so it was, declares the Lord God. And you took your sons and your daughters, whom you had borne to me, and these you sacrificed to them to be devoured.
God made similar statements elsewhere in the Old Testament (see, e.g., Jeremiah 2), explaining that He bestowed many gifts on people yet we forsook Him and in doing so incurred His just punishment. The fact that God repeatedly punishes people says more about humanity's sinfulness than God's Wrath. He chastised people because they forsook Him, but He did not forsake humanity.
As for Jesus in the New Testament, while it's easy to see God's Love and Mercy in Jesus' healing miracles, forgiveness of sins, willingness to suffer and die for us, etc., Jesus had some harsh words, too, and talked quite a bit about hell. For example:
You have heard that it was said to those of old, 'You shall not murder; and whoever murders will be liable to judgment.' But I say to you that everyone who is angry with his brother will be liable to judgment; whoever insults his brother will be liable to the council; and whoever says, 'You fool!' will be liable to the hell of fire.
This passage suggests that in the Old Testament God was actually a bit more permissive than He truly demands of us, and in the New Testament God reveals that He actually demands perfection. Jesus' words about hell suggest that it is actually quite easy for us to end up in hell, which a cursory reading might lead us to believe that God is not so merciful and loving in the New Testament.
A careful reading of both the Old and New Testaments teaches us that God is always loving and merciful but also pours out His Wrath upon unrepentant sinners.