There's a lot of theology to unpack in answering that but I'll have a go! Please bear with me if this gets lengthy...
First off the concept of sin is there by implication in your question. It's probably easiest to think of someone who embodies that in a really obvious way, but at the same time I don't want to trigger too much outrage so let's take an example of someone who mugs old ladies (i.e. bad/upsetting but not Hitler-tier), is unrepentant and a really horrible person by many other metrics as well. Do they go 'straight to heaven' when they die? That seems wrong in two ways, from the Christian POV because nothing unholy (which has a sense of 'unwhole', unwholesome, unclean etc) will ever enter heaven. Heaven may be a literal place, I don't know, but a way of looking at it is that such a person can't 'enter into' the fullness of life we are promised with God, which you could also call the Kingdom of God. Quite possibly they wouldn't want to or be able to bear it.
The second reason is that it doesn't satisfy our sense of retributive justice. We're not perfectly just of course but we do have a sense of fairness which reflects God's justice, so that is a reasonable objection IMO.
So the short answer would be no. And the Bible does talk about judgement. Take the example of Jesus saying to his followers that you should try to be reconciled with an adversary who is taking you to court while you are still on your way there, otherwise you might be handed over to the judge and taken away into prison. "Truly I tell you, you will not get out until you have paid the last penny." So there is potential for quite a harsh punishment there, but not an endless punishment or a death sentence. Taking Jesus at his word, the punishment would actually be in proportion with the crime down to the last penny. But unless you've somehow committed an infinitely enormous sin I can't see how it makes sense for the punishment to last forever, and the words are not that you would never get out, but not until the debt is repaid in full.
Other passages on judgement talk about destruction, or 'perishing', but it's important to recognise that the Greek word used means something like withering away, and in several parables this same word is used to describe souls while they are lost but who are then found and restored (the prodigal son and the lost sheep were both in this state of 'perishing', before they were joyfully restored).
The word used for punishment in the parable of the sheep and the goats comes from the Greek word for pruning, and was used and understood as a corrective punishment in which metaphorically the dead or diseased elements were pruned away to allow for healthy growth. So this would be a difficult and rigorous process but it doesn't imply a final condemnation.
In terms of duration, I don't think time necessarily has the same function after death but it is described as lasting 'an age' which is often mistranslated as meaning forever, even though there were other words which do explicitly mean forever. An age (aion) basically lasts as long as it lasts depending on context so it's not terribly specific!
But I think we can be take encouragement from verses like Lamentations, “For no one is cast off by the Lord forever. Although he causes grief, he will have compassion according to the abundance of his steadfast love; for he does not willingly afflict or grieve anyone.” Elsewhere in Isaiah 28 God's punishment is described as 'an alien work', i.e. although a necessary response to sin it is not a reflection of his deepest nature.
So to sum it all up, it seems to me that there is a universal need of repentance (which we can probably accept more easily in the case of our earlier example), and that the presence of the Lord for the unrepentant would itself be a punishment, which we are warned about, but which ultimately has a redemptive purpose.
I can't be more specific but I'm certain it's not some sort of senseless torture, because that would make God monstrous and IMO completely undermine the idea of a loving God. The best explanation I've read is that it's probable that the full weight of the misery caused by our wrongdoing is finally felt. But Jesus still invites us to cast off that burden through faith in him and simply receive forgiveness, and when we're ready, we will all be able to do that.