The September--October 1977 eruption of Kilauea volcano, Hawaii, produced a river of basaltic lava which flowed for several days. A heat transfer probe containing two heat gauges measured the conduction-dominant heat transfer rates from molten lava into a cold probe inserted in an eddy in the lava river. During a 5-min test period the primary heat flux gauge indicated transient-decaying conduction-dominant heat fluxes ranging from 200 kW/m2 down to 50 kW/m2. A secondary heat flux gauge verified that convective heat flux rates, due to either natural of forced convection in the eddy, were of the order of 10 kW/m2 or less. Theoretical calculations of the expected conduction-dominant heat transfer rates between the lave and the probe agree with the experimental data from the primary gauge within an error of 20% or less. The type of information gained from this field experiment is useful in predicting such diverse things as potential energy extraction rates for heat exchangers in lava or magma as well as the thickness of the solid wall of the natural levee containing a lava flow. Future heat transfer experiments should investigate the low convection heat flux range (below 10 kW/m2) in eddys and the much higher forced-confection heat flux range in the main channel of lava rivers.