A boundary value problem of elliptic type, which describes the stationary heat conduction in nonlinear, inhomogeneous and anisotropic media is considered. The matrix function of the above nonlinear problem depends on the unknown.
A comparison principle (which says that any rise of the density of heat sources determines a nondecreasing temperature) is obtained. As a consequence of the comparison principle, a maximum principle is established. A numerical example is considered.