In this paper, we explore the photorefractive crystal with diffusion nonlinearity mechanism covered by self-focusing Kerr-type crystal contacting with dielectric medium. Four types of nonlinear surface TM electromagnetic waves can propagate along the interfaces of such three-layered composite waveguide. The dispersion equations and conditions of existence of the waves depending on waveguide characteristics are analyzed. This allows to find exact and approximate solutions of dispersion equations in different cases and to obtain the dependence of propagation constant of the surface wave in explicit form. Conditions to control the field distribution across the interface planes by varying the waveguide temperature or waveguide optical and structure characteristics are presented.