A very simple redundant structure is subjected to temperature cycling, primarily to determine the influence of the yield stress/temperature relation on its behaviour: the range and periodic time of the temperature cycle are included as subsidiary variables. It is found that improving the strength of the material at elevated temperatures may have the undesirable effect of hastening incremental collapse of the structure, and that the most rapid incremental collapse is not necessarily associated with maximum values for the range and periodic time of the temperature cycle. It is also found that the common assumption that the strength of the material is independent of temperature may in some circumstances be ambiguous, since there may be a sudden discontinuity in behaviour between a structure made from a material having a slight negative strength/temperature gradient and one made from a material having a slight positive gradient.