Optical properties of a model pressed composite (potassium bromide matrix with incorporated ALEX aluminium powder) are experimentally investigated. It is shown that the spectral dependences of total transmittance and diffuse reflectance can be described with allowance for the presence of both individual aluminium nanoparticles and their aggregates with a characteristic radius of 133 nm in a sample. It is found that irradiation of a composite sample by a 1070-nm cw laser initiates nonlinear absorption of radiation by aluminium particles, which is detected by a change in the sample optical density. A model is proposed to describe the effect, which is based on the sample heating and temperature dependence of the optical characteristics of aluminium particles. The calculation results are in qualitative agreement with the observed changes in optical density; hence, the thermal mechanism of nonlinear absorption of electromagnetic radiation by metal particles is applicable to this model system.