This study analyzes the impact of climate change on the performance of continuous reinforced concrete pavement (CRCP) and proposes a method to improve the existing KPRP–CRCP design procedure. Our analysis of monthly mean temperature data from the Seoul Meteorological Station revealed a general increase in temperature from 2001 to 2034, with a more significant increase observed during summer and winter. The existing KPRP–CRCP design method uses the drop temperature (DT) as a key variable. Notably, the increasing monthly mean temperatures owing to climate change tend to decrease the DT that in turn lowers the maximum stress on the pavement slab. This leads to a significant problem: if the traditional design method based on outdated data is used, the predicted number of punchouts will be lower than expected. This can result in an over-reduction in the reinforcement ratio and slab thickness, leading to premature failure and increased maintenance costs. To solve this issue, we introduced a predictive model for the final setting temperature that accounts for monthly and regional characteristics. Applying this model showed that as the temperature increased, the DT and maximum stress proportionally increased. This provided a more realistic prediction of the number of punchouts and addressed the flaws of the existing design method. Furthermore, our analysis of punchout counts based on the construction start month using this predictive model revealed that punchouts were more frequent in summer (July–August) and less frequent in winter (January–February). Based on this, we determined that the optimal seasons for placing continuous reinforced concrete pavements were spring (March–June) and fall (September–November). In situations where the actual construction start month was unknown, we recommended using a conservative design approach based on the design in August, when punchouts were most likely to occur.