Assuming constant water content, linear stress range, and temperatures between 2°C and 80–100°C, creep of aging concrete at normal and elevated varying (or constant) temperatures, a phenomenon of importance for nuclear reactor vessels, is formulated by a rate-type creep law with hidden stresses based on Maxwell chain model of time-variable properties. Dependence of the creep rate upon temperature is expressed with the help of activation energies which, in general, may be different for the individual Maxwell units in the chain. Introducing the equivalent hydration period, acceleration of aging due to temperature rise is formulated by means of the activation energy of hydration. It is demonstrated that all of the pertinent more extensive data available in the literature can be fitted satisfactorily by the method described. However, no set of data for one concrete available at present is complete enough to assure unique solution to the problem of identification of material parameters from data.