Abstract <p>The development of hydrodynamics mathematical models has led to the need to take into account changes of the physical properties of liquids during its flow under the external factors influence. Currently, anomalously thermoviscous liquids with a non-monotonic temperature dependence of viscosity are of particular interest. Such liquids can be found among natural compounds and modern polymeric materials including superstructural thermoplastics melts used in additive manufacturing and methylcellulose-based solutions used for flow-diverting technologies in oil industry. The paper presents the numerical modeling results of anomalously thermoviscous liquids flow in a narrow annular gap driven by constant pressure drop. The mathematical model is based on the generalized Navier–Stokes equations describing the heat-conducting liquid flow taking into account variable viscosity. It is assumed that the viscosity dependence on the deformation rate can be neglected. This assumption is fulfilled for the case of weakly concentrated aqueous solution of polymers or suspensions flows. The influence of the parameters of the viscosity dependence on temperature on the flow rate dynamics of anomalously thermoviscous liquids was investigated. For this purpose, three model liquids with temperature dependence of viscosity in the form of a Gaussian function with different values of full width at half maximum (FWHM) in an annular channel were considered. The real anomalous temperature dependence of viscosity for a micellar solution of the cationic surfactant EHAC and the binding salt SHNC was also considered as well. Oscillatory regimes of flow rate change of anomalously thermoviscous liquids over time were discovered. It has been shown that both damped and undamped nonlinear flow rate self-oscillations can appear depending on the value of the parameter FWHM and pressure drop. In some cases, undamped oscillations have been identified as Thomson-type self-oscillations.</p>