Does Malachi 4:1 and Jude 7 prove that hell is temporary? Does Malachi 4:1 and Jude 7 prove that hell is temporary?
I'm studying the bible and I found a few verses that seem to challenge the idea of an eternal hell forever and ever. Even though the bible says forever and ever and eternal. (Mark 3:29, Revelation 20:10)
These are the verses I'm referring to... (Malachi 4:1, Jude 7)
Malachi 4:1 
“For behold, the day is coming,
Burning like an oven,
And all the proud, yes, all who do wickedly will be stubble.
And the day which is coming shall burn them up,”
Says the Lord of hosts,
“That will leave them neither root nor branch.
Jude 7 
as Sodom and Gomorrah, and the cities around them in a similar manner to these, having given themselves over to sexual immorality and gone after strange flesh, are set forth as an example, suffering the vengeance of eternal fire.
So having noted the verses, here is my question. Malachi 4:1 says that the wicked will be burned up and will have neither root nor branch, and Jude 7 tells us that Sodom was an example and that the city of Sodom had eternal fire which is obviously not burning today.
So is hell temporary or eternal?
Before we delve into what Malachi and Jude said, remember that two verses plucked out of the Bible can never establish whether a doctrine is right or wrong. These things have to be put into context and many other Scriptures must be consulted before a full picture emerges.
Malachi carries on from where the prophets Haggai and Zechariah left off.  The setting is the return of the Jews to Jerusalem and the rebuilding of the temple. The time is about 445 years before the birth of Jesus. Malachi rebukes the Jews who doubt the love of God and the faithlessness of both people and priests.  After promising to send his messenger to prepare the way (John the Baptist) for God’s messenger of the covenant (Jesus), Malachi warns the Jews of the judgement to come.  Remember that this prophecy of judgment is directed first and foremost to God’s own people, to those who would reject the messenger of the covenant.
Malachi uses a literary device to paint a word picture of what this day will be like.  When he says “it will burn like a furnace” and “every evildoer will be stubble” and “not a root or a branch will be left”, we can visualise a field that has been burned after the crop has been gathered.  Nothing will be left.  Malachi is not speaking about the eternal destination of the wicked on the final Day of Judgment.
Almost 500 years later, after the life, death and resurrection of Jesus (the messenger of the covenant), Jude writes to the very first Christians to remind them of how God delivered his people out of Egypt, but later destroyed those who did not believe.   He speaks of how the people of Sodom and Gomorrah were killed because of their immorality and perversions.

In a similar way... They serve as an example of those who suffer the punishment of eternal fire.

The fire that came down from heaven on Sodom and Gomorrah was not eternal, but it utterly destroyed the wicked inhabitants of that region.  Jude refers to historical events as an illustration.
The two Bible verses you quote do not suggest that hell is either temporary or eternal.   The book of Revelation has much to say about the Day of Judgment and the final destination of those people who fail to repent and who continue to blaspheme God.