In his Commentary on Matthew, Mark, and Luke, John Calvin identified Gehenna with hell. He wrote on the word Gehenna used by Jesus in Matthew 5:22: 
Those, again, who break out into reproaches are adjudged to the hell of fire: which implies, that hatred, and every thing that is contrary to love, is enough to expose them to eternal death, though they may have committed no acts of violence. Γἔεννα (hell) is, beyond all question, a foreign word. גיא (Ge) is the Hebrew word for a valley. Now, “the valley of Hin-nom” was infamous for the detestable superstition which was committed in it, because there they sacrificed their children to idols, (2 Chronicles 33:6). The consequence was, that holy men, in order to excite stronger hatred of that wicked ungodliness, used it as the name for hell, that the very name might be dreaded by the people as shocking and alarming. It would appear that, in the time of Christ, this was a received way of speaking, and that hell was then called by no other name than gehenna, (γέεννα,) the word being slightly altered from the true pronunciation.
The “holy men” Calvin refers to, who replaced the word Jesus used with hell, are represented in Daniel’s prophecy of chapter 7 by the little horn, with “eyes like the eyes of a man, and a mouth speaking great things.” The “eyes like the eyes of a man” represent a human viewpoint as opposed to a divine one.
Jesus used the word Gehenna because it was associated with Jerusalem, and so its meaning is limited to the things connected with the holy city, the heavenly Jerusalem, and with the gospel. It does not apply to the world as Calvin thought.
Calvin wrongly applied the word Gehenna to unbelievers, who were not called by God, in his Institutes of the Christian religion.  He wrote:
In order that we may quickly summarize the whole matter, let this stand as the first of two distinctions: wherever punishment is for vengeance, there the curse and wrath of God manifest themselves, and these he always withholds from believers. On the other hand, chastisement is a blessing of God and also bears witness to his love, as Scripture teaches. This distinction is sufficiently pointed out through all God’s Word. For all the afflictions that the impious bear in the present life depict for us, as it were, a sort of entry way of hell, from which they already see afar off their eternal damnation. And yet they are so far from changing themselves on this account, or profiting by it at all, that by such preliminaries they are rather prepared for the dire Gehenna that at last awaits them.
It is clear that no Gehenna can await the unbeliever, or the person who had never heard the gospel preached, as one has to be in Jerusalem to be cast out of it. The unbeliever who has never been called, or enlightened by the gospel, has no part in Gehenna. The warnings about Gehenna apply to the church, which is the heavenly Jerusalem, not the world. Calvin was mistaken. In another place he declared that Gehenna is eternal.
But because there is no adequate description to demonstrate how horrible the suffering of the wicked will be, the torments which they must bear are put in images of physical things, that is, darkness, tears, groans, gnashing of teeth, eternal fire, and worms constantly gnawing the heart (Isa. 66:24). For it is certain that the Holy Spirit intended by these ways of speaking to indicate an extreme horror which might move all the senses; as when He says that a deep Gehenna is prepared for them for all eternity, with blazing fire for which there is always wood ready to keep it going and the Spirit of God like a blast of air to kindle it (Isa. 30:33)
Jesus said the fire is not quenched; the fire is his word. Several scriptures say God’s word endures forever.
1 Peter 1:25
But the word of the Lord endureth for ever. And this is the word which by the gospel is preached unto you.
Jesus said, “Heaven and earth shall pass away: but my words shall not pass away.” [Mark 13:31] This is what the fire of Gehenna alludes to.
When Jesus used the word Gehenna, he used it in the sense that Jeremiah’s prophecies about the valley of the son of Hinnom had associated with it. God had said that bringing forth children, only to have them burned in a fire, was something that had never come into his mind.
And they built the high places of Baal, which are in the valley of the son of Hinnom, to cause their sons and their daughters to pass through the fire unto Molech; which I commanded them not, neither came it into my mind, that they should do this abomination, to cause Judah to sin.
The sin of the people who practiced this abomination was one of the main reasons they were removed from the promised land, and taken into exile in Babylon. And similar practices by the Canaanites dwelling in the land were one of the reasons they had been dispossessed by the Israelites. The implication is, Christians who embrace the idea of unending infernal torment attribute to God a thing which has never come into his mind. Thus, they miss the promised rest that the land represents. The spiritual significance of the land promise was perceived by Calvin, as he wrote:
Hence, when he chose Abraham, Isaac, and Jacob, and their posterity, to the hope of immortality, he promised them the land of Canaan for an inheritance, not that it might be the limit of their hopes, but that the view of it might train and confirm them in the hope of that true inheritance, which, as yet, appeared not. And, to guard against delusion, they received a better promise, which attested that this earth was not the highest measure of the divine kindness. Thus, Abraham is not allowed to keep down his thoughts to the promised land: by a greater promise his views are carried upward to the Lord. He is thus addressed, “Fear not, Abram: I am thy shield, and thy exceeding great reward,” (Gen. 15: l.) Here we see that the Lord is the final reward promised to Abraham that he might not seek a fleeting and evanescent reward in the elements of this world, but look to one which was incorruptible. A promise of the land is afterwards added for no other reason than that it might be a symbol of the divine benevolence, and a type of the heavenly inheritance, as the saints declare their understanding to have been. Thus David rises from temporal blessings to the last and highest of all, “My flesh and my heart faileth: but God is the strength of my heart, and my portion for ever.” “My heart and my flesh crieth out for the living God,” (Ps. 73: 26; 84: 2.) Again, “The Lord is the portion of mine inheritance and of my cup: thou maintainest my lot,” (Ps. 16: 5.) Again “I cried unto thee O Lord: I said Thou art my refuge and my portion in the land of the living,” (Ps. 142: 5.) Those who can venture to speak thus, assuredly declare that their hope rises beyond the world and worldly blessings. This future blessedness, however, the prophets often describe under a type which the Lord had taught them.
In the prophecy of Jeremiah, Gehenna, referred to as “the whole valley of the dead bodies,” is to eventually become “holy unto the Lord.” [Jeremiah 31:40]
2. John Calvin. Institutes of the Christian religion, Book 3 chapter 4 Sect. 32.
3. John Calvin, Jean Calvin, Elsie Anne McKee. Institutes of the Christian religion: 1541 French edition. Wm. B. Eerdmans Publishing, 2009. p. 267.
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