One of the more intriguing solutions of General Relativity is the C-metric, which can be interpreted as describing the spacetime of an accelerating black hole. Little is known about the thermodynamics of these objects. Here I present a consistent formulation of the thermodynamics of accelerated black holes, resolving inconsistencies and discrepancies that have appeared in previous investigations of this subject. Their thermodynamic volume obeys the reverse isoperimetric inequality for all values of the parameters. The dual stress-energy tensor for the spacetime corresponds to a relativistic fluid with a non-trivial viscous shear tensor.