During the Last Glacial Maximum, tropical sea surface temperatures were 1 to 3C cooler than present, but the altitude of the snowlines of tropical glaciers was lower than would be expected in light of these sea surface temperatures. Indeed, both glacial and twentieth-century snowlines seem to require lapse rates that are steeper than a moist adiabat. Here we use estimates of Last Glacial Maximum sea surface temperature in the Indo-Pacific warm pool based on the clumped isotope palaeotemperature proxy in planktonic foraminifera and coccoliths, along with radiative-convective calculations of vertical atmospheric thermal structure, to assess the controls on tropical glacier snowlines. Using extensive new data sets for the region, we demonstrate that mean environmental lapse rates are steeper than moist adiabatic during the recent and glacial. We reconstruct glacial sea surface temperatures 4 to 5C cooler than modern. We include modern and glacial sea surface temperatures in calculations of atmospheric convection that account for mixing between rising air and ambient air, and derive tropical glacier snowlines with altitudes consistent with twentieth-century and Last Glacial Maximum reconstructions. Sea surface temperature changes ≤3C are excluded unless glacial relative humidity values were outside the range associated with deep convection in the modern. We conclude that the entrainment of ambient air into rising air masses significantly alters the vertical temperature structure of the troposphere in modern and ancient regions of deep convection. Furthermore, if all glacial tropical temperatures were cooler than previously estimated, it would imply a higher equilibrium climate sensitivity than included in present models. © 2014 Macmillan Publishers Limited.