Measurements of the heat capacity of single crystals of Ba0.6K0.4 BiO3 in the range 1040 K and in magnetic fields up to 60 kOe reveals a jump at Tc. The phase diagram of Hc2(T) can thus be determined calorimetrically, yielding values of Tc(H=0)=31.5 K and dHc2/dT=-5.2 kOe/K, in agreement with recent magnetization measurements. From these data, and the value of dHc1/dT from magnetization data, the size of the jump is consistent with at least 40% of the sample volume becoming a superconductor, indicating that superconductivity in this material is a bulk property and not due to a trace amount of a second phase. The corresponding value of the electronic specific-heat coefficient is =1.5 mJ/mol K2. Comparison with the band-structure density of states yields a value of the electron-phonon coupling constant of 0.35, consistent with the assumption that the material is a weakly coupled superconductor.