Holographic dual of pure-classical systems

Question

There are classical systems (eg. see Sections VII and VIII of Kogut's review that shares many of the properties of a pure-gauge SU(N) quantum theory including factorization and mass-gap, but with inverse temperature (rather, $J/T \sim \beta$) playing the role of coupling constant.

In such classical systems, what would its holographic dual (if any) look like, especially since temperature is already assigned another role in normal thermal AdS/CFT.

Note: I am not referring to thermal QFT, but classical spin systems with local symmetry (like O(3) model in 2D, for example, which coincidentally inspired the first QCD strings).