Are wrinkles\folds in paper reversible by heat, pressure or something else? I ran into this question on Lifehacks.SE, regarding how to remove wrinkles from a crumpled piece of paper. Suggestions included ironing the paper or placing it under some heavy books for a few days.

I am wondering about the chemistry of these processes and whether they are actually effective. This Reddit thread gives some general background about the molecular structure of paper and what happens when you fold paper with enough force to permanently create folds, i.e. to break bonds (as opposed to rolling it within the "elastic boundaries", as it says there). See also this excellent infographic from Compoundchem.

So, can ironing\applying pressure really straighten out a folded paper back to factory level? If not, is there any other way to unwrinkle a paper?

I'd appreciate explanations in the molecular level.
Once you fold a paper or crush a paper, then it was found experimentally that the internal geometry of paper developed ridges throughout inside it and these ridges inside the folded or crushed paper holds the energy you imparted by folding the paper. This energy imparted by you by folding the paper gets stored in the ridges of the paper in form of bending energy (and this bending energy is also the reason that a crumpled paper ball cannot be further compressed beyond around 90% air). 

The crumpling of a piece of paper leaves localised permanent marks. This shows that, by some mechanism, the crumpling has focused the stress at some points, exceeding there the limit yield of the material and leading thus to irreversible deformations.

Indeed, a piece of crumpled paper does not usually return to its planar shape even if you iron it or apply pressure to it because along the folds, the material is often strained beyond the level of reversible elasticity.