Are wrinkles\folds in paper reversible by heat, pressure or something else?
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.