Heating of trapped ion clouds by interactions with free electrons crossing the trapping potential was observed. A model describing such process was proposed and discussed. The presented approach predicts two effects: pushing and heating of the ions' ensemble by electrons. The former was found to be too weak for observation, however the latter was investigated experimentally. For comparison between experimental results and theoretical predictions, molecular dynamics simulations for various ion ensembles in various temperatures were performed to determine dependence between ion cloud geometry and its temperature. A heating rate coefficient was defined and determined together with temperatures of ion clouds bombarded with electrons. Good correlation between the two quantities was found, which agrees with the proposed model. * lklos@fizyka.umk.pl