The numerical formulation of Shaw, Hamilton, and Peck (p. 384-414 of this issue) using the method of explicit cell balances was applied to the cooling of Alae lava lake, Hawaii. Temperatures in this 15-m-thick, ponded basalt flow were measured over a 4-yr period from 1 week after it formed in August 1963 at a temperature of 1140 degrees C until temperatures throughout the lake had fallen to below 100 degrees C. Representative temperature profiles in the thicker central part of the lake can be reproduced with average deviations of 21 degrees C using one-dimensional models with a lake thickness of 14.6 m, a constant diffusivity of 0.006 cm 2 /sec, a latent heat of 90 cal/g, and a heat withdrawal of 620 cal/cm2 of measured rainfall using the average measured density of basalt in the lake in the calculations. Average differences between computed and observed temperature profiles were decreased to 2 degrees C by using all the following modifications of the initial model: (1) diffusivity was allowed to vary according to the calculated increase of the heat capacity with temperature, the variations of the measured density of the lava with depth in the lake, and the variations of conductivity with temperature and lava porosity; (2) heat loss to rainwater was computed using the measured density structure of the lake; (3) the lake thickness was increased to 14.9 m, a better approximation of the deepest part of the lake, and the latent heat of the basalt was accordingly decreased; and (4), low conductivity and density values were assigned to one of the cells to simulate the highly vesicular and cavernous zones found at shallow depth in the lake. The best results were obtained using a latent heat of 80 + or - 10 cal/g (from 80 percent crystallization of the lava) and a conductivity that increased with temperature at a rate of 0.06 + or - 0.01 percent of its value at room temperature per degree C. Computations using a two-dimensional model indicate that marginal cooling decreased temperatures in the lake more than 1 degrees C only in the outer 15 m of the lake until a year after the eruption and only in the outer 45 m during the final year of cooling. The values for latent heat and conductivity derived from the thermal modeling are in good agreement with values determined directly in the laboratory and calculated from laboratory data.