In rubber friction studies, it is often observed that the kinetic friction coefficient μ depends on the nominal contact pressure p. We discuss several possible origins of the pressure dependency of μ: (1) saturation of the contact area (and friction force) due to high nominal squeezing pressure; (2) nonlinear viscoelasticity; (3) nonrandomness in the surface topography, in particular the influence of the skewness of the surface roughness profile; (4) adhesion; and (5) frictional heating. We show that in most cases the nonlinearity in the μ(p) relation is mainly due to process (5), frictional heating, that softens the rubber, increases the area of contact, and (in most cases) reduces the viscoelastic contribution to the friction. In fact, because the temperature distribution in the rubber at time t depends on the sliding history (i.e., on the earlier time t′ < t), the friction coefficient at time t will also depend on the sliding history, that is, it is, strictly speaking, a time integral operator. The energy dissipation in the contact regions between solids in sliding contact can result in high local temperatures that may strongly affect the area of real contact and the friction force (and the wear-rate). This is the case for rubber sliding on road surfaces at speeds above 1 mm/s. Previously, we derived equations that described the frictional heating for solids with arbitrary thermal properties. Here, the theory is applied to rubber friction on road surfaces. Numerical results are presented and compared to experimental data. We observe good agreement between the calculated and measured temperature increase.