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The linear-$T$ resistivity is one of the hallmarks of various strange metalsregardless of their microscopic details. Towards understanding this universalproperty, the holographic method or gauge/gravity duality has made muchprogress. Most holographic models have focused on the low temperature limit,where the linear-$T$ resistivity has been explained by the infrared geometry.We extend this analysis to high temperature and identify the conditions for arobust linear-$T$ resistivity up to high temperature. This extension isimportant because, in experiment, the linear-$T$ resistivity is observed in alarge range of temperatures, up to room temperature. In the axion-dilatontheories we find that, to have a robust linear-$T$ resistivity, the strongmomentum relaxation is a necessary condition, which agrees with the previousresult for the Guber-Rocha model. However, it is not sufficient in the sensethat, among large range of parameters giving a linear-$T$ resistivity in lowtemperature limit, only very limited parameters can support the linear-$T$resistivity up to high temperature even in strong momentum relaxation. We alsoshow that the incoherent term in the general holographic conductivity formulaor the coupling between the dilaton and Maxwell term is responsible for arobust linear-$T$ resistivity up to high temperature.

Linear-$T$ resistivity from low to high temperature: axion-dilaton theories