In spite of a remarkable progress in recent years made in modeling and characterizing the concrete fatigue behavior, many open questions remain that need to be fundamentally addressed in order to develop a deep and general insight into the phenomenology of concrete fatigue. The fatigue behavior of concrete is usually studied as a separate phenomenon. However in reality the fatigue deformation during the fatigue life is influenced by the creep and time dependent viscous effects as observed experimentally. Therefore, a consistent reflection of fatigue-creep interaction phenomenon is essential for a realistic modeling of concrete fatigue behavior. In addition to the fatigue-creep interaction, the loading rate shows a considerable influence on concrete behavior under both monotonic and fatigue loading. Alongside fatigue-creep interaction, the loading rate significantly influences concrete behavior under both monotonic and fatigue loading. To the best of the authors' knowledge, no existing model adequately captures the interaction of these effects with the cyclic and fatigue behavior of concrete. This contribution aims to introduce a unified, thermodynamically-based constitutive model describing the behavior of inter-aggregate within the concrete microstructure, capable of encompassing the aforementioned interacting effects. The model will integrate viscoelastic and viscoplastic behavior with cumulative sliding damage as a driving mechanism for fatigue and material degradation. Additionally, temperature will be considered as an extra state variable within the thermodynamic framework, evolving due to the accumulation of time-dependent viscoplastic strains, representing the heat generation due to internal friction within the material structure. Elementary studies of the proposed formulation will be presented to analyze the interacting time-dependent and thermal effects within monotonic and cyclic behavior. Subsequently, the model will be applied to study the bond behavior between concrete and reinforcement, considering various loading scenarios and rates, with comparisons to experimental results provided. In the future, the model will be applied within microplane and lattice discrete models, enabling a comprehensive description of time- and temperature-dependent fatigue behavior in concrete.