Cooling rates have been determined for basaltic glasses from different depths of the submarine section of the drill core recovered in the 1999 phase of Hawaii Scientific Drilling Project (HSDP2). The glasses include degassed blocky hyaloclastite clasts and undegassed pillow rims. The degassed glassy clasts were generated in subaerial or shallow submarine environments, during explosive interactions between lava and seawater, before eventual deposition under water. The volatile contents of the glassy pillow rims are consistent with eruption and quenching in water several hundred metres deep. The cooling rates have been calculated from the calorimetric properties of the glass across the glass transition. The heat capacity ( c p ) of each sample was measured during several cycles of heating from room temperature to temperatures above their glass transition using a differential scanning calorimeter (DSC). Their compositions did not change during the thermal treatment, a prerequisite for successful c p measurements, although the glasses with higher H 2O contents became more opaque and their mid-IR spectra changed. Each c p - T path exhibits the now classic features of the glass transition; glassy and liquid states separated by a hysteresis marking the transition. After experiencing the same experimental thermal history the glass transition occurs at lower temperatures in glasses with higher H 2O contents. Except for one sample, the c p - T path measured on initial heating also releases energy stored during the natural quench, which is not recovered during subsequent experimental cooling. The energy stored in the HSDP2 glasses is much less than that observed in hyperquenched natural and synthetic glasses. Even so, the Tool–Narayanaswamy enthalpy relaxation geospeedometer, usually used to determine the cooling rates in volcanic glasses, is unable to deal with this energy release. For those samples that exhibit this feature an alternative method, developed for hyperquenched glasses, is applied. This uses the energy released to calculate T f , from which the cooling rate is calculated. The degassed blocky hyaloclastite clasts exhibit cooling rates 0.1–72.2 K s −1, while the undegassed pillow rims span 0.2–46.4 K s −1. The fastest cooling rates are consistent with the cooling of lava bodies in seawater. The wide variation for both types of glass could reflect quenching at different distances from the basalt-seawater interface. However, for the degassed hyaloclastite clasts the range could indicate that the clasts were generated by different processes operating during the explosive interaction between lava and seawater in the littoral zone. In the undegassed pillow lavas, glassy rims may have been reheated, giving rise to more complex, slower, thermal histories, as a result of latent heat released during the crystallisation of pillow interiors, or flow replenishment. Both types of glass may also have experienced reheating from succeeding flows or deposits. Compared to deep-sea limu o Pele hyaloclastite fragments, whose hyperquench rates indicate simultaneous cooling and fragmentation, the shallow blocky hyaloclastite clasts may have formed during post-cooling brittle fragmentation.