Tires are the only contact points between a vehicle and the road, and they are mainly responsible for the driving safety. Currently, two different classes of friction formulations are predominant: phenomenological and micromechanical. Phenomenological approaches formulate a mathematical expression to describe the experimental results. By knowledge and experience, the formulations interpolate and extrapolate the behavior captured by experiments; however, the formulations are highly dependent on the quality and the influence factors of the experiments. In micromechanical approaches, the friction kinematics is described based on the deformation of the rubber in the contact zone, while sliding over a generalized surface. The basic idea is to obtain the friction coefficient solely by the surface properties and the material behavior. Because both approaches have advantages and disadvantages, it is hard to distinguish which is more suitable to use in a certain application. In this contribution, different friction formulations are discussed and compared. The mechanical behavior of rubber is strongly influenced by temperature and so are its friction characteristics; therefore, the friction formulations are expanded with respect to temperature. The discussed temperature dependent friction formulations are compared with each other for tire cornering simulations. The decrease of the cornering stiffness at large slip angles can be explained by friction-induced temperature increase in the contact zone.