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The adiabatic evolution of the temperature of the cosmic microwave background(CMB) is a key prediction of standard cosmology. We study deviations from theexpected adiabatic evolution of the CMB temperature of the form $T(z)=T_0(1+z)^{1-\alpha}$ using measurements of the spectrum of the SunyaevZel'dovich Effect with the South Pole Telescope (SPT). We present a method forusing the ratio of the Sunyaev Zel'dovich signal measured at 95 and 150 GHz inthe SPT data to constrain the temperature of the CMB. We demonstrate that thisapproach provides unbiased results using mock observations of clusters from anew set of hydrodynamical simulations. We apply this method to a sample of 158SPT-selected clusters, spanning the redshift range $0.05 < z < 1.35$, andmeasure $\alpha = 0.017^{+0.030}_{-0.028}$, consistent with the standard modelprediction of $\alpha=0$. In combination with other published results, weconstrain $\alpha = 0.011 \pm 0.016$, an improvement of $\sim 20\%$ overpublished constraints. This measurement also provides a strong constraint onthe effective equation of state in models of decaying dark energy$w_\mathrm{eff} = -0.987^{+0.016}_{-0.017}$.

Constraints on the CMB Temperature Evolution using Multi-Band Measurements of the Sunyaev Zel'dovich Effect with the South Pole Telescope