Heating may well add some flexibility to the high-surface area interfaces at the boundaries from glass to plexi and back. Most of the change of behavior would be in the plastic layers and the bonding adhesives between plastic and glass. The overall rigidity of the glass would not be much affected, but the ability of the composite assembly to accept impact shock waves and dissipate them safely to successive layers and to the frame structure would be heightened.
Heating on the way up and down would also help relieve the inter-layer thermal stresses in the windshield panels. Fractures often result as release of the combined energy of impact plus stored internal stress.
Do not know this for certain, but it seems consistent with the behavior of the materials in the typical window sandwich.