The thermal histories of two subglacial rhyolite glasses from Torfaj¿kull complex of south central Iceland have been determined from changes in the relaxation of enthalpy in the calorimetric glass transition interval. Heat capacity measurements of bulk glass samples from Rau¿ufossafj¿ll (sample number JS.1.1) and Bl¿hn¿kur (sample number JS.2.1) by differential scanning calorimetry show marked differences in the temperature of the onset of glass transition (Tg) on reheating. The average Tg is 750 K for JS.1.1, whereas it is 850 K for JS.2.1. These differences in the onset of Tg are related to quench rate through considerations of the activation energy and timescales for structural relaxation modeled, using the Kohlrausch-Williams-Watt function. Multiple glass samples from the two Torfaj¿kull locations recover different average values and distributions of a fictive temperature, Tf, which we interpret in terms of differences in the thermal histories of the glasses. In both glass samples the range of fictive temperatures and, by implication, apparent cooling rates, is lower than those estimated for a glass rapidly quenched by contact with cold (glacial melt) water and requires that the glass was annealed at temperatures in the glass transition interval associated with relaxation times of the order of 1000--10,000 s. The complex cooling histories of the Torfaj¿kull samples show that the products of subglacial eruptions may be held at elevated temperatures for several hours and, as a result, may drive vigorous convection in the ice-bound vaults above erupting rhyolite deposits.