In this study, the compressive behavior of concrete cores detached from the high-strength concrete-filled steel tube (CFST) members reinforced with steel fibers and containing crumb tire rubber was investigated experimentally after exposure to elevated temperatures. The test variables included the diameter-to-thickness ratio of the steel tube, volume content of crumb rubber replacing natural sand, volume fraction of steel fibers, and temperature. After the exposure of the CFST specimens to the elevated temperatures and subsequently removing the steel tubes, the detached concrete core was subjected to the axial compression test, and the parameters of compressive strength, modulus of elasticity, strain at peak stress, and weight loss, stress-strain relationship together with the ultrasonic pulse velocity, visual appearance, and failure mode were evaluated. Using the experimental results, expressions were developed to predict the mechanical properties of the concrete core at elevated temperatures taking into account the steel tube wall thickness. The findings indicated that increasing the thickness of the steel tube had a greater damaging effect on the heated concrete core, while in the fiber-reinforced specimens, this damaging effect was lower. Moreover, the addition of crumb rubber to the concrete mix as the natural sand replacement degraded the mechanical properties of the heated and unheated concrete core.