Elijah going to heaven

Many people believe heaven is some mysterious place in the sky where God lives. Commonly people assume that when your body die, your "immortal" soul will continue to live there. Often artists would create pictures of golden gates in clouds as some sort of entrance into "heaven". These ideas potentially originated from the Greek mythology that described Elysium as such a place where heroes and gods continue to live after death.

Many people believed Elijah went directly to this kind of heaven without dying based on the scripture:

And as they still went on and talked, behold, chariots of fire and horses of fire separated the two of them. And Elijah went up by a whirlwind into heaven. And Elisha saw it and he cried, “My father, my father! The chariots of Israel and its horsemen!” And he saw him no more. -- 2 Kings 11:12 (ESV)

The original Israeli who lived in Elijah's time were not influenced by Greek mythology like us. To them, "heaven" is the sky. For example:

He blotted out every living thing that was on the face of the ground, man and animals and creeping things and birds of the heavens. -- Genesis 7:23 (ESV)

and

And at the seventh time he said, “Behold, a little cloud like a man's hand is rising from the sea.”
And he said, “Go up, say to Ahab, ‘Prepare your chariot and go down, lest the rain stop you.’”

And in a little while the heavens grew black with clouds and wind, and there was a great rain.

-- 1 Kings 18:44-45 (ESV)

and

For as the rain and the snow come down from heaven and do not return there but water the earth... -- Isaiah 55:10 (ESV)

The apostles also referred to "heaven" as the sky. For example:

We also are men, of like nature with you, and we bring you good news, that you should turn from these vain things to a living God, Who made the heaven and the earth and the sea and all that is in them. In past generations he allowed all the nations to walk in their own ways. Yet he did not leave himself without witness, for he did good by giving you rains from heaven ... -- Acts 14:15-17 (ESV)

The prophets did not consider that Elijah as entered some sort of realms of gods, but instead they thought he would eventually be set down somewhere else. That is why they looked for him (2 Kings 2:16).

While others wanted to search for Elijah, Elisha understood that if God had wanted Elijah there, He would not have moved him. Understanding the customs of the time further helps to clarify this section of Scripture. God had told Elijah to anoint Elisha to succeed him (1 Kings 19:16). According to custom, Elisha could not assume leadership of the prophets as long as Elijah was present. Therefore, in order to allow Elisha to lead, God had to find a way to graciously remove Elijah. He chose to do it by a whirlwind. Elijah was not taken up to the place where God lives, but he was taken up into the air and placed somewhere else. God simply moved Elijah from one place to another and he lived out his days somewhere else. Elijah could not have been taken to heaven to live with God because he lived before the time of Christ. It is Christ’s shed blood that is the only valid payment for all men’s sin, including Elijah’s. If Elijah were already enjoying everlasting life in heaven, there was no need for Christ to come and to die for his sin. -- Spirit and Truth International

Elijah could not have gone to heaven, because John wrote:

No one has ascended into heaven except he who descended from heaven, the Son of Man. -- John 3:13 (ESV)

Rewards in heaven

There are many verses that mention a reward in heaven like:

Rejoice and be glad, for your reward is great in heaven... -- Matthew 5:12 (ESV)

and

Do not lay up for yourselves treasures on earth, where moth and rust destroy and where thieves break in and steal, but lay up for yourselves treasures in heaven, where neither moth nor rust destroys and where thieves do not break in and steal. -- Matthew 6:19-20 (ESV)

and

... the hope laid up for you in heaven. -- Colossians 1:5 (ESV)

and

According to His great mercy, He has caused us to be born again to a living hope through the resurrection of Jesus Christ from the dead, to an inheritance that is imperishable, undefiled, and unfading, kept in heaven for you ... -- 1 Peter 1:3-4 (ESV)

Possible explanations:

• "Heaven" is some sort of protective dimension or place where God stored our rewards in our absence. God will provide these reward in some future time, perhaps on the "new earth" or at a special event.
• "Heaven" is a Hebrew idiom for something that is good. So when the reward is "in heaven", it means it is a very good reward.
• Our rewards are not gifts, but instead it is God's respect and love for us. Jesus referred to God as "Our Father in Heaven" and our reward is to be with Him.
• Our rewards are distinctive gifts, but they are safe with God Who is in heaven. In other words, nobody from Earth can steal, damage or touch our rewards because it is not affected by the events on Earth.