Knowledge of the magnitude of the Last Glacial Maximum (LGM) cooling is a useful constraint for estimating the climate sensitivity used in projecting future climate change. Proxy comparison, especially that between the alkenone-based U-37(K ') and the archaeal tetraether-based TEX86, has been increasingly applied in paleoceanographic studies as a measure to better constrain proxy-derived temperature estimates. In this study, we compile and compare published multiproxy (U-37(K ') and TEX86H) records of glacial cooling measured on the same sediment cores. In spite of the diversity in oceanographic and sedimentation settings spanned by the study sites, we find that the TEX86H-derived mean tropical LGM cooling is approximately twice as strong as that suggested by the U-37(K ') and MARGO estimates. The extent of proxy discrepancy varies with the application of various regional calibrations, but the mean TEX86H-inferred cooling remains stronger than that inferred from U-37(K '). To understand the discrepancy between proxies, we examine the seasonal and water column structure of LGM cooling simulated by state-of-the-art climate models. We find that the dissimilar magnitudes of proxy-derived glacial cooling cannot be fully explained by proxies reflecting temperature of different seasons or different water depths, if the recording season and depth are assumed to stay constant through time. A hypothetical shift in recording season and/or depth between the Holocene and the LGM could in theory cause the proxy discrepancy, but this hypothesis cannot be constrained due to a lack of information on lipid production and export in the water column during the LGM. Alternatively, the systematic proxy discrepancy, which persists across diverse oceanographic settings, may imply that the commonly applied proxy calibrations for reconstructing past temperatures are fundamentally biased. As evidenced by the improved consistency between U-37(K ') and TEX86H-based estimates of LGM cooling after we applied a global subsurface (0-200 m) temperature calibration for TEX86H, it is plausible that the TEX86H signal originates from deeper in the water column than typically assumed for the proxy calibration.