The rheological behavior of heavy oils is critical for oil exploitation in different stages, such as extraction, transportation, and refining; during this process, the oil undergoes temperature changes that directly affect the viscosity. For light oils, the viscosity decreases around 1 order of magnitude when the temperature increases 100 K, whereas for heavy oils, this change could be of more than 3 orders of magnitude for the same temperature increment. Furthermore, the heavy oils exhibit a viscoelastic behavior, usually characterized by a viscosity reduction with the increment in the shear rate, the presence of elasticity, and time-dependent rheological behavior. As the temperature increases, the oils acquire a Newtonian behavior. This change is illustrated with the rheological characterization of five heavy oils with an American Petroleum Institute (API) gravity around 12°, different compositions, and zero-shear viscosity that varies up to 2 orders of magnitude among oils. The measurements were carried out in a controlled stress rheometer using a 40 mm parallel plate geometry with a gap of 1 mm. The fluids were tested in rotational and oscillatory modes at temperatures from 5 to 100°C. In the oscillatory experiments, the loss and storage moduli, associated with viscosity and elasticity, respectively, are presented. Above a transition temperature, not only does the viscosity decrease but also the normal force and the elastic modulus tend to vanish, suggesting that the non-Newtonian behavior is also strongly related to the temperature. Furthermore, the departure from linearity of the logarithm of zero-shear viscosity versus the inverse of the temperature appears to correlate with the transition from non-Newtonian to Newtonian behavior.