Monitoring thermal processes occurring in molecular films on surfaces can provide insights into physical events such as morphology changes and phase transitions. Here, we demonstrate that temperature-programmed contact potential difference (TP-∆CPD) measurements employed by a Kelvin probe under ultrahigh vacuum conditions and their temperature derivative can track films' restructure and crystallization occurring in amorphous solid water (ASW) at temperatures well below the onset of film desorption. The effects of growth temperature and films' thickness on the spontaneous polarization that develops within ASW films grown at 33 K-120 K on top of a Ru(0001) substrate are reported. Electric fields of ∼106 V/m are developed within the ASW films despite low average levels of molecular dipole alignment (<0.01%) normal to the substrate plane. Upon annealing, an irreversible morphology-dependent depolarization has been recorded, indicating that the ASW films keep a "memory" of their thermal history. We demonstrate that TP-∆CPD measurements can track the collapse of the porous structure at temperatures above the growth and the ASW-ice Ic and ASW-ice Ih transitions at 131 K and 157 K, respectively. These observations have interesting implications for physical and chemical processes that take place at the interstellar medium such as planetary formation and photon- and electron-induced synthesis of new molecules.