We have studied electric field heating of low‐dimensional electrons in GaAs/AlGaAs heterostructures at 4.2 K using thermal noise measurements. For the two‐dimensional (2D) wire, the increase in electron temperature, &Dgr;Te, extracted from noise measurements is in agreement with previous measurements of &Dgr;Teand is explained by emission of acoustic and optical phonons. Measurements are extended to quasi‐one‐dimensional (Q1D) wires which are shorter than the 2D wires. In these Q1D wires, we find that for small &Dgr;Te, power dissipation is more effective than in the 2D wires, due to additional energy relaxation through the contacts. This effect is most pronounced in the highest mobility wire where the energy relaxation length is the longest. ©1995 American Institute of Physics.