The acceleration of thermal solar wind protons at spherical interplanetary shocks driven by coronal mass ejections is investigated. The solar wind velocity distribution is represented using $kappa$-functions, which are transformed in response to simulated shock transitions in the fixed-frame flow speed, plasma number density, and temperature. These heated solar wind distributions are specified as source spectra at the shock from which particles with sufficient energy can be injected into the diffusive shock acceleration process. It is shown that for shock-accelerated spectra to display the classically expected power-law indices associated with the compression ratio, diffusion length scales must exceed the width of the compression region. The maximum attainable energies of shock-accelerated spectra are found to be limited by the transit times of interplanetary shocks, while spectra may be accelerated to higher energies in the presence of higher levels of magnetic turbulence or at faster-moving shocks. Indeed, simulations suggest fast-moving shocks are more likely to produce very high-energy particles, while strong shocks, associated with harder shock-accelerated spectra, are linked to higher intensities of energetic particles. The prior heating of the solar wind distribution is found to complement shock acceleration in reproducing the intensities of typical energetic storm particle events, especially where injection energies are high. Moreover, simulations of $sim$0.2 to 1 MeV proton intensities are presented that naturally reproduce the observed flat energy spectra prior to shock passages. Energetic particles accelerated from the solar wind, aided by its prior heating, are shown to contribute substantially to intensities during energetic storm particle events.
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