Can humans fall in love with each other in heaven? How does falling in love work in heaven? Do we still fall in love? 

Is it possible to fall in love with more than one person? Or are we set to love just one person or none at all? Are intimate relationship in allowed heaven at all? Is having sexual relationship allowed in heaven?  Or, is heaven just a sexless, harp-playing place?  

In other words, what is the role of sex and love between humans in heaven, beyond the place of the love for God?
So, there are passages that are particularly relevant here:


Matthew 22:29 - 32


  29 Jesus replied, “You are in error because you do not know the Scriptures or the power of God. 30 At the resurrection people will neither marry nor be given in marriage; they will be like the angels in heaven. 31 But about the resurrection of the dead—have you not read what God said to you, 32 ‘I am the God of Abraham, the God of Isaac, and the God of Jacob’[b]? He is not the God of the dead but of the living.”


From this we know that there is no marriage but that doesn't say there isn't love.
1 Corinthians 13:12


  12 For now we see through a glass, darkly; but then face to face: now I know in part; but then shall I know even as also I am known.


Historically there has been an interpretation of this verse that says our current understanding of love is highly limited - our sinful nature is such that we are capable only of a simulcrum of love, one which gets jealous when it reaches more than one, and one which is held back by our fleshly nature.  In contrast, in heaven, where there is perfection, we are able to love more deeply more fully than here. 


Indeed, C.S. Lewis' The Great Divorce explores this theme, suggesting an almost open kind of love that is neither pornographic nor chaste.  Mere Christianity picks this up, saying:


  The sins of the flesh are bad, but they are the least bad of all sins. All the worst pleasures are purely spiritual: the pleasure of putting other people in the wrong, of bossing and patronising and spoiling sport, and backbiting; the pleasures of power, of hatred. For there are two things inside me, competing with the human self which I must try to become. They are the Animal self, and the Diabolical self. The Diabolical self is the worse of the two. That is why a cold, self-righteous prig who goes regularly to church may be far nearer to hell than a prostitute. But, of course, it is better to be neither.


He develops this further, saying that sex is a second thing, not a first one. InFirst and Second Things, he shows that sex is spiritual, but that made an end unto itself, it loses its meaning. As Peter Kreeft writes:


  It could certainly be spiritual intercourse—and, remember, that includes sexual intercourse because sex is spiritual. This spiritual intercourse would mean something more specific than universal charity. It would be special communion with the sexually complementary; something a man can have only with a woman and a woman only with a man. We are made complete by such union: "It is not good that the man should be alone." And God does not simply rip up His design for human fulfillment. The relationship need not be confined to one in Heaven. Monogamy is for earth. On earth, our bodies are private. In Heaven, we share each other's secrets without shame, and voluntarily. In the Communion of Saints, promiscuity of spirit is a virtue.


In short, the idea of heaven in this understanding is that sex will be way more open, the complete perscription to the diagnosis in Genesis that it is not good for the man to be alone. 

If this is true, we'll be getting way more, and way better sex up there than down here. Whether or not this is physical, whether or not this is even true, the real point is that anyone who is simply convinced there can't be sex in heaven does have a bit of theology against which to contend.