This paper presents results of studies of the problem to describe the nature of oil flow at low temperatures and shear velocities for prediction of flow fluidity and determination of the parameters of a cold start of an oil pipeline after an extended downtime. Analytical and experimental studies have been carried out, which include a review of rheological test data from earlier studies available in the literature and an analysis of empirical relation obtained with the rotational viscometry method. More specifically, the existence of a zone of viscosity anomaly for low-paraffin and heavy oils has been proved on the basis of laboratory test data of model mixtures of commercial crude oils and their weighted samples. The necessity has been substantiated to create more adaptive rheological models which fit the total curve of oil flow, including the zone of viscosity anomaly in the transient state of cold start, this zone manifesting itself when reaching a certain temperature, even for low-paraffin oils. Based on the results of this work, the most advance multi-factor rheological models have been identified for description of the total shape of the rheological curve in a wide range of temperatures and velocities.