The FLOWGO thermo-rheological model links heat loss, core cooling, crystallization, rheology and flow dynamics for lava flowing in a channel. We fit this model to laser altimeter (LIDAR) derived channel width data, as well as effusion rate and flow velocity measurements, to produce a best-fit prediction of thermal and rheological conditions for lava flowing in a ~1.6 km long channel active on Mt. Etna (Italy) on 16th September 2004. Using, as a starting condition for the model, the mean channel width over the first 100 m (6 m) and a depth of 1 m we obtain an initial velocity and instantaneous effusion rate of 0.3--0.6 m/s and ~3 m3/s, respectively. This compares with field- and LIDAR-derived values of 0.4 m/s and 1--4 m3/s. The best fit between model-output and LIDAR-measured channel widths comes from a hybrid run in which the proximal section of the channel is characterised by poorly insulated flow and the medial-distal section by well-insulated flow. This best-fit model implies that flow conditions evolve down-channel, where hot crusts on a free flowing channel maximise heat losses across the proximal section, whereas thick, stable, mature crusts of 'a'a clinker reduce heat losses across the medial-distal section. This results in core cooling per unit distance that decreases from ~0.02--0.015¿C m-1 across the proximal section, to ~0.005¿C m-1 across the medial-distal section. This produces an increase in core viscosity from ~3800 Pa s at the vent to ~8000 Pa s across the distal section.