We have employed noise thermometry for investigations of thermal relaxation between the electrons and the substrate in nanowires patterned from 40-nm-thick titanium film on top of silicon wafers covered by a native oxide. By controlling the electronic temperature T e by Joule heating at the base temperature of a dilution refrigerator, we probe the electron-phonon coupling and the thermal boundary resistance at temperatures T e = 0.5 − 3 Kelvin. Using a regular T 5 -dependent electron-phonon coupling of clean metals and a T 4 -dependent interfacial heat flow, we deduce a small contribution for the direct energy transfer from the titanium electrons to the substrate phonons due to inelastic electron-boundary scattering.