The relevance of the study is due to the need to develop technological and technical solutions of protecting from paraffin and gas hydrate plugs within the pipelines formed under particular thermohydrodynamic conditions. In this regard, this article is aimed at disclosing the features of heating and melting of such plugs using a super-high-frequency electromagnetic radiation source moving within the pipeline. A theoretical study of temperature change within the "pipeline -plug -environment" system, which allows us to fully consider its interaction with the electromagnetic radiation, is the leading method for studying this problem. A mathematical model has been presented and a theoretical study of the plug electromagnetic heating process for heat exchange on the pipe outer surface according to Newton's law on the hypothesis that the EM transmitter of Н11 type moves, and the achievement of a complicated configuration of thermal sources and temperature has been disclosed in the article. The materials of the article are of practical value for establishing the initial indices of the paraffin plugs removal technology in a pipeline and oil well when exposed to electromagnetic radiation.