Theoretical estimates of the temperature distributions are obtained in structures where thin copper films mounted on special membrane wafer transmission electron microscopy (TEM) specimens are exposed to low energy (63–114 eV) ion bombardment in a magnetically enhanced (ME) plasma reactor. The substrate temperatures are experimentally measured as a function of rf power in the plasma reactor and of time. The temperature rise in the copper films is obtained based on a two‐dimensional heat transfer finite element analysis with input of a heat flux at the surface due to ion bombardment. The results indicate that copper heating due to ion bombardment is minimal because of rapid heat transfer through the underlying structure and the observed microstructural changes in copper films during plasma processing must be attributed to other causes. ©1995 American Institute of Physics.