The physical origin of the overionized recombining plasmas (RPs) in supernova remnants (SNRs) has been attracting attention because its understanding provides new insight into SNR evolution. However, the process of the overionization, although it has been discussed in some RP-SNRs, is not yet fully understood. Here we report on spatially resolved spectroscopy of X-ray emission from IC~443 with {it XMM-Newton}. We find that RPs in regions interacting with dense molecular clouds tend to have lower electron temperature and lower recombination timescale. These tendencies indicate that RPs in these regions are cooler and more strongly overionized, which is naturally interpreted as a result of rapid cooling by the molecular clouds via thermal conduction. Our result on IC~443 is similar to that on W44 showing evidence for thermal conduction as the origin of RPs at least in older remnants. We suggest that evaporation of clumpy gas embedded in a hot plasma rapidly cools the plasma as was also found in the W44 case. We also discuss if ionization by protons accelerated in IC~443 is responsible for RPs. Based on the energetics of particle acceleration, we conclude that the proton bombardment is unlikely to explain the observed properties of RPs.