A heat flow equation with beam-induced heating and various cooling processes for a carbon wire passing through a particle beam is solved. Due to equation nonlinearity a numerical approach based on discretization of the wire movement is used. Heating of the wire due to the beam-induced electromagnetic field is taken into account. An estimation of the wire sublimation rate is made. The model is tested on SPS, LEP and Tevatron Main Injector data. Results are discussed and conclusions about limits of Wire Scanner operation on LHC beams are drawn
