We construct a simple, spherical blast wave model to estimate the pressure structure of the intergalactic medium surrounding hyperstarburst galaxies, and argue that the effects of interaction with star-forming galaxy winds may be approximated at early times by an adiabatically expanding, self-similar ‘bubble’ as described by Weaver et al. and Ostriker & McKee. This model is used to make observational predictions for the thermal Sunyaev-Zel'dovich effect in the shocked bubble plasma. Radiative cooling losses are explored, and it is found that bremsstrahlung will limit the epoch of adiabatic expansion to 10⁷- 10⁸ yr: comparable to total hyperstarburst lifetimes. Prospects for making a first Sunyaev-Zel'dovich detection of galaxy wind bubbles using the Atacama Large Millimeter Array are examined for a number of active hyperstarburst sources in the literature.