Processes of concentration and separation of calcium and magnesium from artificial and natural sea water by carboxylic ion-exchange resins of acrylic and methacrylic types at different temperatures have been investigated. The values of equilibrium separation factor alpha for Ca2+-Na+, Mg2+-Na+ and Ca2+-Mg2+ exchanges in ternary systems have been determined in the temperature range of 10 degrees C to 80 degrees C. A significant increase of alpha values at elevated temperatures has been observed in the first two cases while for Ca2+-Mg2+ exchange less remarkable temperature dependence of alpha can be distinguished. This effect has been shown to allow a selective thermostripping of Ca2+ and Mg2+ from the resins equilibrated at 80 degrees C with sea water in applying cool sea water at 10 degrees C. The thermostripping leads to a selective desorption of both Ca2+ and Mg2+ while Na+ ions remain sorbed, resulting in the increase of Ca2+ and Mg2+ concentration in the eluate up to 50% (in comparison with the initial sea water) and a decrease of 10% for Na+ concentration. These results may be considered as unique in polythermal concentration in comparison with, e.g. conventional evaporation technique. The results of consecutive sorption-thermostripping cycles have shown the possibility to concentrate calcium and magnesium from natural sea water more than three times by applying reagentless (and wasteless as a result) ion-exchange technique. The results of frontal separation of Ca2+ and Mg2+ on acrylic resin in Na+-form from natural sea water and thermostripping solutions obtained are also presented. The novel approach for forecasting temperature dependences of the resin selectivity has been proposed. The approach is based on a thermodynamic interpretation of the results obtained that allows to predict the temperature dependences of both alpha (for binary Mg2+-Na+ exchange) and the apparent equilibrium constant of ternary Na+-Ca2+-Mg2+ exchange.