There has been some discussion on shot noise, which ultimately referred to Art of Electronics 2nd ed. ch 7.11. The "current in a simple resistive circuit has far less noise than predicted by the shot-noise formula." I have not looked into this issue for a while but reading up on stuff I could get my hands on, it looks like electron-phonon interaction length is short enough at room temperature to guarantee that electrons thermalize with the metal lattice, thus enabling the shot noise to be suppressed. The interesting bit is when the resistor length drops below the electron-phonon length, as long as transport is not ballistic, the shot noise is only partially suppressed (factor of 1/3 for the independent hot electron case and sqrt(3)/4 for the interacting hot electron case).
Fred