Understanding the intricate relationship between illumination and temperature in metallic nano-particles is crucial for elucidating the role of illumination in various physical processes which rely on plasmonic enhancement but are also sensitive to temperature. Recent studies have shown that the temperature rise in optically thick ensembles of metal nanoparticles under intense illumination is dominated by the thermal conductivity of the host, rather than by the optical properties of the metal or the host. Here, we show that the temperature dependence of the thermal conductivity of the host dominates the nonlinear photothermal response of these systems. In particular, this dependence typically causes the temperature rise to become strongly sublinear, reaching even several tens of percent. We then show that this effect can explain experimental observations in several recent plasmon-assisted photocatalysis experiments. Under certain conditions, we show that thermal emission may also contribute to photothermal nonlinearity. This shows that any claim for the dominance of non-thermal electrons in plasmon-assisted photocatalysis must account first for this photothermal nonlinear mechanism.