Heat conduction in silicon can be effectively engineered by means of sub-micrometre porous thin free-standing membranes. Tunable thermal properties make these structures good candidates for integrated heat management units such as waste heat recovery, rectification or efficient heat dissipation. However, possible applications require detailed thermal characterisation at high temperatures which, up to now, has been an experimental challenge. In this work we use the contactless two-laser Raman thermometry to study heat dissipation in periodic porous membranes at high temperatures via lattice conduction and air-mediated losses. We find the reduction of the thermal conductivity and its temperature dependence closely correlated with the structure feature size. On the basis of two-phonon Raman spectra, we attribute this behaviour to diffuse (incoherent) phonon-boundary scattering. Furthermore, we investigate and quantify the heat dissipation via natural air-mediated cooling, which can be tuned by engineering the porosity.