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 UK'37 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 (UK'37 and TEXH86) 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 TEXH86-derived mean tropical LGM cooling is approximately twice as strong as that suggested by the UK'37 and MARGO estimates. The extent of proxy discrepancy varies with the application of various regional calibrations, but the mean TEXH86-inferred cooling remains stronger than that inferred from UK'37. 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 UK'37 and TEXH86-based estimates of LGM cooling after we applied a global subsurface (0-200 m) temperature calibration for TEXH86, it is plausible that the TEXH86 signal originates from deeper in the water column than typically assumed for the proxy calibration.