We consider a process of filling of a long plane slit by a chemically solidificated (rheo-kinetic) fluid. The process is accompanied by a two-dimensional impregnation of porous anisotropic (reinforcing) layer. We take into account the relationship of the viscosity coefficient on temperature and on the rate of chemical solidification. Temperature fields in the region of a split and in the porous layer are related to each other by conjugated boundary conditions of the fourth order. We study how non-isothermal and kinetic factors affect the rate and the properties of processes of infilling and impregnation.