Will we theoretically be able to sin in Heaven?

God has free will. We have been made in the image of God. Thus, we have free will. (Obviously, this does not directly address the arguments against this position.) There is absolutely no reason to think that we will no longer have free will, in the next life.

Free will implies the (theoretical) possibility of evil. As "Steven" says (approximately), it is strongly true that God will never sin, because He is holy — not just good, but positively and powerfully opposed to evil. Conversely — having free will — it is theoretically possible for Him to do evil. (If it were not theoretically possible for Him to do evil, then there would be little kudos or glory in Him so not doing. (A robot that never does evil is not morally good, on account of being a (deterministic) machine.) )

As “Fofole” notes, in the question, “The Bible tells us that there will be no sin in Heaven.”

It follows that the reason for this (absence of evil) is for some reason other than that it is not theoretically possible.

My view (behind which there is a lot of thinking) is as follows.

The fact of evil arising — noting that this took place in Heaven (apart from the connotation that this denotes the next life) — was strongly anomalous — for some of the reasons that it would be anomalous in “Heaven” [here meaning the next life]. That is… evil is bad — it has bad effects (by definition) — and this would be strongly apparent (before the deed) in Heaven. Thus, the idea of doing evil, in Heaven, would have negative appeal. [Actually, that is a simplification (possibly an oversimplification).] [Of course, conversely, one must have some account of why then Satan would do this.]

Under my view, this would have even greater negative appeal in Heaven in the next life, on account of the lesson of seeing evil in action on Earth — to the point that nothing else would be needed, practically. (One element of this is the [then now] clear historical event and illustration that there is a Fall involved — that the possibility does not exist, of simply doing one evil act.)

Over and above that, though, (under my view) anyone who attempted to sin in “Heaven” — here meaning the next life — would be instantly cast into Hell.

Very simply, yes.

Spirit creatures have free will just like humans and as such can and do sin. Like Adam and Eve, spirit creatures started out perfect, without sin, so when they use thier free will and deliberately give into their wrong desires and break the laws of the one who gave them life, they sin (James 1:15), and the wages of sin is death (Romans 6:23). That is where Satan and his demons come from.

Jesus could have sinned also, that is why is is the Bible says the Devil tested him (Luke 4:13), if he couldn't have sinned would it really have been a test? Regarding humans who receive the heavenly calling, they will be granted imortality, (1 Corinthians 15:54) in this way they will never die. That is why the gift of immortality is such a vote of confidence on God's part because he is saying that he trusts these ones, including Jesus, totally, and he is absolutely sure that they will never choose a life apart from him.

I think the Bible declares there will be no sin evermore but keeps the exact mechanism from our view. I wholly agree with Caleb, that the cause is not prevention of temptation but our new nature will be immune to temptation while still having free will.

Although the scripture does not explain the answer I think it does assume that this 'immunity to sin' is due to our life being derived from Christ. The first Adam communed with God but God was not eternally united with him via the incarnation. Therefore Adam's free will included the option of breaking the communion.

The second Adam has free will but not a freedom to sin because God was 'locked' as it were into his own person via the incarnation. Therefore those reborn have their life sprung from a human source that can't break communion with God. As our life is in Christ, we can't unlock our person from communion with God. In this world we have both natures as not our while life from Adam has died and resurrected yet.

A tree can't 'will' to be a fish and someone in Christ can't will himself to be someone else. We are 'locked in' without loosing our free will. Free will is not an infinite power that can break the bonds of the incarnation, or the origin and container of our own person. It is easier for a human to 'chose' to be a turtle than for a man or woman in heaven to sin.

I think Romans 8:29-30 gives us a bit of a hint of the mechanism of this:

Romans 8:29 For those whom he foreknew he also predestined to be conformed to the image of his Son, in order that he might be the firstborn among many brothers. 30 And those whom he predestined he also called, and those whom he called he also justified, and those whom he justified he also glorified.

There is some theological disagreement on specifics of the Ordo Solutis, but I think it is generally agreed that Christians who have been justified will be glorified as well -- and, thus fully conformed to the image of Jesus. At the end of that process, our glorified selves will then be without sin. In this sense, we will be unable to sin in the same way that Christ is unable to sin.

There's some philosophical elements that add murkiness to definitions here: there was no external constraint placed on Jesus that prevented him from sinning (so, in that sense, he was theoretically able to sin), but rather his perfect nature would not allow for it (so, in that sense, he was not functionally able to sin). Caleb's answer deals with this. An analogy might be something like a lion eating a salad: Sure he's free to do so, but his nature would never entertain such a thought, so to do so would require a drastic change of his nature or a violation of his will. With our glorified nature (conformed to that of Jesus), we will have no desire to sin, and so any sin that would be theoretically possible would be so only if our natures were changed or our wills violated. In heaven, there's no reason to believe either of these things would occur.