A temperature perturbation method for a direct Monte Carlo simulation of the residual free energy is extended to the isothermal—isobaric ensemble. Unlike many other free energy or phase equilibrium methods, particle insertion is avoided. At the same time, the usual Boltzmann sampling is maintained. The results show excellent agreement with equations of state and thermodynamic integration for fluids of hard dumbbells and linear chains of tangent hard spheres. The results cover states at which insertion techniques fail.