Joint, volume-weighted distribution of the temperature and density of baryons in our simulation at z = 2.2. Center: the fiducial (T₀, γ) parameter case (values obtained by fitting a power-law through gas temperatures and densities). Left: the case with rescaled temperatures for a lower γ than the fiducial and the same T₀. This can be seen to affect the slope of the TDR by a twisting of the 2D distribution. Right: the case with rescaled temperatures for a higher T₀ than the fiducial and the same γ. The entire distribution is shifted along the log₁₀(T/K) axis, keeping the shape the same. (Note that the color-bar label is using shorthand for $p({\log }_{10}\left({\rho }_{\mathrm{b}}/{\overline{\rho }}_{\mathrm{b}}\right),{\log }_{10}(T/\mathrm{K}))$.)