Recent X-ray studies have revealed overionized recombining plasmas in a dozen mixed-morphology (MM) supernova remnants (SNRs). However, the physical process of the overionization has not yet been fully understood. Here we report on spatially resolved spectroscopy of X-ray emission from W44, one of the overionized MM SNRs, using XMM-Newton data from deep observations, with the aim of clarifying the physical origin of the overionization. We find that combination of low electron temperature and low recombination timescale is achieved in the region interacting with dense molecular clouds. Moreover, a clear anticorrelation between the electron temperature and the recombination timescale is obtained from each of the regions with and without the molecular clouds. The results are well explained if the plasma was overionized by rapid cooling through thermal conduction with the dense clouds hit by the blast wave of W44. Given that a few other overionized SNRs show evidence for adiabatic expansion as the major driver of the rapid cooling, our new result indicates that both processes can contribute to overionization in SNRs, with the dominant channel depending on the evolutionary stage.