We have carried out Joule heating measurements on three etched quantum wires (QWRs) of various widths and 2D electron gases (2DEGs) over temperatures ranging from 0.035 K to 20(.)K. The devices are fabricated in an InAlAs/InGaAs/InAlAs heterostructure with a 25 nm wide In0.53Ga0.47As quantum well region, grown on a lattice matched InP substrate. Comparison of the Shubnikov-de Haas oscillations (SdHO) in the wires and 2DEGs and the phase-breaking time (from conductance fluctuations) in the narrowest wire are used to extract the temperature dependence of the power loss per electron. (C) 2004 American Vacuum Society.