We analyse Chandra X-ray Observatory observations of a set of galaxy clusters selected by the South Pole Telescope using a new publicly available forward-modelling projection code, MBPROJ2, assuming hydrostatic equilibrium. By fitting a power law plus constant entropy model we find no evidence for a central entropy floor in the lowest entropy systems. A model of the underlying central entropy distribution shows a narrow peak close to zero entropy which accounts for 60 per cent of the systems, and a second broader peak around 130keVcm2 . We look for evolution over the 0.28–1.2 redshift range of the sample in density, pressure, entropy and cooling time at 0.015R500 and at 10 kpc radius. By modelling the evolution of the central quantities with a simple model, we find no evidence for a non-zero slope with redshift. In addition, a non-parametric sliding median shows no significant change. The fraction of cool-core clusters with central cooling times below 2 Gyr is consistent above and below z = 0.6 (~30–40 per cent). Both by comparing the median thermodynamic profiles, centrally biased towards cool cores, in two redshift bins, and by modelling the evolution of the unbiased average profile as a function of redshift, we find no significant evolution beyond self-similar scaling in any of our examined quantities. Our average modelled radial density, entropy and cooling-time profiles appear as power laws with breaks around 0.2R500. The dispersion in these quantities rises inwards of this radius to around 0.4 dex, although some of this scatter can be fitted by a bimodal model.