Strength of lead rubber bearings (LRBs) deteriorates as a function of temperature rise in the lead core under cyclic motions. Accordingly, the isolator exhibits a gradual change in its hysteretic behavior that affects both the energy dissipation capacity and lateral strength of isolator. Thus, the superstructure response may change due to variation in the characteristics of LRB. This paper focuses on the effects of lead core heating on the superstructure response of seismically isolated buildings (SIBs) in terms of peak floor accelerations and story drift ratios. A parametric study was performed for two different seismically isolated buildings by conducting bounding analyses (non-deteriorating hysteresis loops for LRBs) and temperature-dependent analyses (deteriorating hysteresis loops for LRBs). A 20-story reinforced concrete (RC) and a 3-story steel structure were subjected to earthquake excitations to assess the effects of isolator properties such as isolation period and characteristic strength-to-weight ratio on the superstructure response. Results revealed that the success of bounding analyses to provide a safe envelope for superstructure response depends on the characteristics of SIB. (C) 2017 American Society of Civil Engineers.