Amorphous to crystalline: Opposite trend?
What they say in your book is right. Take the case of polyethylene terephthalate (PET) which is a kind of polyester used in water bottles for example. It's an amorphous polymer (remember the bottles are transparent). When it is heated, the strained chains have the possibility to move and reorder themselves and the polymer becomes partially crystalline. This fact can readily be proved experimentally by heating a piece of PET (over its glass transition temperature, around $74 ^0\mathrm{C}$), then quenching the sample. It becomes white and not transparent which means it's partially crystalline.
We can monitor this transformation using a specific instrument called differential scanning calorimeter, where we can notice the formation of an exothermic peak corresponding to crystallization.