The thermal gas treatment of a reservoir is a promising technology for oil recovery from kerogencontaining rocks of the Bazhenovo Formation. It is expected that this treatment can form a kerogen pyrolysis area, which will advance in the direction of filtration flow. The pyrolysis will result in an increase in rock porosity. An analogue of this process from the viewpoint of hydrodynamics can be melting of part of the material of the matrix of a permeable rock by heat due to the filtration stream having a high temperature. The paper presents results of an experimental study on the melting-front propagation dynamics for a part of the framework material during filtration of a hot viscous fluid through the material. The formation and propagation of the melting front as melted "fingers" and the phenomenon of rim formation from the molten matter at melting front are described.