Data on the variation of temperature with time and in space are essential to a complete understanding of the crystallization history of basaltic magma in Kilauea Iki lava lake. Methods used to determine temperatures in the lake have included direct, downhole thermocouple measurements and Fe-Ti oxide geothermometry. In addition, the temperature variations of MgO and CaO contents of glasses, as determined in melting experiments on appropriate Kilauean samples, have been calibrated for use as purely empirical geothermometers and are directly applicable to interstitial glasses in olivine-bearing core from Kilauea Iki. The uncertainty in inferred quenching temperatures is ??8-10?? C. Comparison of the three methods shows that (1) oxide and glass geothermometry give results that are consistent with each other and consistent with the petrography and relative position of samples, (2) downhole thermo-couple measurements are low in all but the earliest, shallowest holes because the deeper holes never completely recover to predrilling temperatures, (3) glass geothermometry provides the greatest detail on temperature profiles in the partially molten zone, much of which is otherwise inaccessible, and (4) all three methods are necessary to construct a complete temperature profile for any given drill hole. Application of glass-based geothermometry to partially molten drill core recovered in 1975-1981 reveals in great detail the variation of temperature, in both time and space, within the partially molten zone of Kilauea Iki lava lake. The geothermometers developed here are also potentially applicable to glassy samples from other Kilauea lava lakes and to rapidly quenched lava samples from eruptions of Kilauea and Mauna Loa. ?? 1987 Springer-Verlag.