Why plastic sheets contract when heated?
When plastic sheets are produced, they are rapidly cooled to keep the polymer chains oriented in a way that makes the sheets nice and flat. This is a relatively high-strain orientation since it is associated with the energy level of the molecules at the casting temperature.

Once the plastic is heated above its glass transition temperature, the polymer chains are no longer locked in that high strain orientation. They relax to a low energy orientation- curled and bending in a way that shrinks the bulk material.

As for the precise mechanism, I'm not exactly sure. I would guess that the shrunken conformation is entropically favorable because there are more arbitrary bends. This would decrease the Gibbs free energy, making it a more stable shape.

Alternatively, it could be that hydrogen bonding between chain elements makes the folded shape more enthalpically favorable.