Heat-capacity, X-ray diffraction, and resistivity measurements on a high-quality BaFe2As2 sample show an evolution of the magneto-structural transition with successive annealing periods. After a 30-day anneal the resistivity in the (ab) plane decreases by more than an order of magnitude, to 12 µΩcm, with a residual resistance ratio ∼36; the heat-capacity anomaly at the transition sharpens, to an overall width of less than K, and shifts from 135.4 to 140.2 K. The heat-capacity anomaly in both the as-grown sample and after the 30-day anneal shows a hysteresis of ∼0.15 K, and is unchanged in a magnetic field µ0H = 14 T. The X-ray and heat-capacity data combined suggest that there is a first order jump in the structural order parameter. The entropy of the transition is reported.