Residual strains and shape distortions in a polymer-based composite structure may depend on the cure schedule used for manufacture. Aiming to understand the cure history effects, the influence of the curing “path” (time (Formula presented.) and temperature (Formula presented.) path during curing) on viscoelastic (VE) response of a fully cured (FC) ((Formula presented.) = 0.992) epoxy was investigated. Five different “families” of the same epoxy were manufactured in constraint-free conditions using different sets of curing parameters. Then, tensile tests were performed at different temperatures (T = 30 to 110 °C), and the time–temperature superposition principle (TTSP) and Schapery’s type of linear viscoelastic (VE) model, accounting for physical aging of specimens tested at high temperature, were used. The results show that the VE properties of the studied epoxy are independent of the curing history provided that at the end all specimens are fully cured. Also, the physical aging rate at high temperatures of all “families” is the same and it can be described by a simple aging-temperature independent equation reported in Nunes et al.1 It is expected that curing history of unconstrained and fully cured epoxy has an insignificant effect on final viscoelastic behavior, a knowledge which could assist in developing more time and cost-efficient cure cycles.