We report on the generation of high-power narrow-bandwidth terahertz (THz) pulses by cryogenic cooling of hand-made periodically poled lithium niobate (PPLN) wafer stacks. As a proof-of-concept, we cool stacks with up to 48 wafers down to 97 K and achieve few-percent bandwidths at a center frequency of 0.39 THz, with pulse energy up to 0.42 mJ and average power of 21 mW. Supported by modeling, we observe effective cooling of PPLN wafer stacks that not only reduces terahertz absorption but critically maintains the micrometer-scale inter-wafer gaps for optimal terahertz transmission. Our results unlock the potential for scaling these large-area sources to greater numbers of wafers to push both the energy and bandwidth beyond current capability, opening up possibilities in areas such as terahertz-driven particle acceleration, terahertz imaging, and control over material properties.