  Understanding the intricate relation 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 can explain experimental
observations in several recent plasmon-assisted photocatalysis experiments.
This shows that any claim for dominance of non-thermal electrons in
plasmon-assisted photocatalysis must account first for this photothermal
nonlinear mechanism.
