Irradiation of a solid with intense plasma-ion beams produced within a high vacuumchamber (by the so-called Rod Plasma Injector [1]) is a strongly nonequilibrium process, which enablesachieving a number of effects which are impossible to be achieved with other methods. These are,amongst other: improvement of ceramics wettability, fabrication of stable copper-ceramics interfacesand stable Ni-Cu and Al-Cu interfaces, improvement of tribological properties and high temperatureoxidation resistance of stainless steel, photovoltaic junction formation, and many others. In the paper,the process of plasma-ion beam propagation regarding its time and energy distributions and the processof ion penetration of solids, resulting with ion implementation and temperature growth have beenanalyzed mathematically on basis of experimental data. Results of numerical calculations have beenpresented concerning temperature and dopant density time evolution.