In solar thermochemical redox cycles for H2O/CO2-splitting, a large portion of the overall energy demand of the system is associated with heating the redox material from the oxidation temperature to the reduction temperature. Hence, an important measure to improve the efficiency is recuperation of sensible heat stored in the redox material. A solid-solid heat exchanger can be subject to undesirable oxygen crossover, which decreases the oxygen uptake capacity of the redox material and consequently the system efficiency. We investigate the extent of this crossover in ceria based cycles, to identify, under which conditions a heat exchanger that allows oxygen crossover can improve the system efficiency. In a thermodynamic analysis we calculate the amount of transferred oxygen as a function of the heat exchanger efficiency and show the system efficiency of such a concept. A second law analysis is applied to the model to check the feasibility of calculated points of operation. For the investigated parameter set the heat exchanger design improves the system efficiency by a factor of up to 2.1.