A mean-field lattice theory is used to predict electrolyte effects on the temperature-concentration phase behavior and structure of an alkyl-propoxy-ethoxylate surfactant in water. The salt ions are treated as charged species interacting with surfactant segments and water via adjustable Flory-Huggins chi-parameters. The surfactant undergoes thermotropic (rather than lyotropic) transitions with a reversal in curvature (from water continuous to alkyl continuous) upon an increase in temperature. This is attributed to the ''graded" nature of the surfactant interactions with water, which originates from the fact that the propoxy and ethoxy groups become progressively more hydrophobic as the temperature increases. The addition of NaCl is found to sharpen the thermotropic phase transitions and to shift them to lower temperatures compared to the salt-free case. The electrolyte effects on the macroscopic phase behavior are reflected in the microscopic information provided by the model on the species volume fraction profiles in the self-assembled domain, the distributions of ends and block junctions, and the domain spacing. The parameters that describe the interactions between the different species are obtained from simple experiments, and thus this theoretical framework can be useful in capturing the effects of various electrolytes on nonionic surfactant phase behavior.