Temporary emigration is widespread in animals and plants and has important implications for ecological processes, evolution and the conservation of species. It is increasingly studied with capture–mark–recapture (CMR) models. Temporary emigration provides particular challenges to CMR analyses if it involves movement to an unobservable state. A multistate model in which individuals may move between an “observable” and an “unobservable” state (called TE model) was developed for such cases. The model assumes equal survival probability in both states. This assumption may be violated, especially if temporary emigration involves trade-offs between survival and reproduction. A comprehensive assessment of the effects of unequal survival probability on power to detect temporary emigration and on bias and precision of estimates is still needed to understand the applicability and limits of the model. We assessed power to detect temporary emigration for four goodness-of-fit tests and evaluated bias and precision of estimates for the TE model and for its combination with a robust design. Our simulation study, based on 16,650 parameter combinations, shows that temporary emigration is more challenging than currently usually acknowledged. The Tests 2.CT and 2.C are largely independent of the difference in survival probability between the states. In contrast, Test 3.SR is sensitive to the difference in survival probability but also to emigration probability. Tests 2.C and 2.CT have high power if a large part of the population temporarily emigrates and a large fraction of the individuals return on the next capture occasion. Under this condition, bias is low and precision adequate even if the assumption of equal survival probability is violated. Bias and precision are also satisfactory if the assumption is met but unsatisfactory or unreliable for the remaining parameter space. We conclude that the uncertainties whether an appropriate model was selected and whether the estimates from the selected model may be biased should be clearly communicated and that every endeavour should be made to make the unobservable state observable.