In this paper the analytical solution of the differential equation, describing viscous incompressible liquid motion through straight round pipe, with one perturbation parameter is given. The perturbation is introduced into the equation through the disturbed viscosity, depending on the temperature. The solution of the corresponding differential equation is sought in the form of a series in the small parameter. Thus the flow reaction to the internal disturbance is studied. The solution, presented in this article, gives an opportunity to further studying the temperature impact on a viscous weakly compressible liquid motion through a pipe. This research may be of interest to the problems of hydrocarbons control flow through main pipelines.