The dissipative characteristics of rubber-cord composites under the action of cyclic load considering the features of their self-heating have been experimentally investigated. Full-scale uniaxial tension experiments are performed on the plane specimens along the reinforcement fibers of the unidirectional rubber-cord composites. In compliance with the test results, stress–strain curves for the specimens are determined, which form the hysteresis loops under cyclic loading. The tensile testing of the specimens is performed under long-term cyclic loading using the experimental setup INSTRON ElectroPuls E3000 Test System. The process of significant self-heating of the specimens under their long-term cyclic deformation has been experimentally established and studied. Using the non-contact methods, the variation in the specimen temperature in time is measured. The mechanisms of their non-stationary heating are obtained, as well as the dependences of the stabilization temperature of the thermal state on the loading conditions. It has been determined that the area of hysteresis loops, which is formed when specimens undergo deformation in the temperature-stabilized state, depends nonlinearly on the amplitude of strains. The qualitative and quantitative dependences of the loss modulus, as well as the dissipation coefficients and relaxation times on the loading frequency, strain amplitude and temperature due to the material self-heating, are determined. The approximation dependences of the loss modulus of the composite on the loading frequency and self-heating temperature are constructed on the basis of the generalized three-parameter linear (Zener) model and the exponential temperature-dependent initial elastic modulus.