We have found a remarkably large response of the transition temperature of CaFe 2 As 2 single crystals grown from excess FeAs to annealing and quenching temperature. Whereas crystals that are annealed at 400 • C exhibit a first-order phase transition from a high-temperature tetragonal to a low-temperature orthorhombic and antiferromagnetic state near 170 K, crystals that have been quenched from 960 • C exhibit a transition from a high-temperature tetragonal phase to a low-temperature, nonmagnetic, collapsed tetragonal phase below 100 K. By use of temperature-dependent electrical resistivity, magnetic susceptibility, x-ray diffraction, Mössbauer spectroscopy, and nuclear magnetic resonance measurements we have been able to demonstrate that the transition temperature can be reduced in a monotonic fashion by varying the annealing or quenching temperature from 400 • to 850 • C with the low-temperature state remaining antiferromagnetic for transition temperatures larger than 100 K and becoming collapsed tetragonal, nonmagnetic for transition temperatures below 90 K. This suppression of the orthorhombic-antiferromagnetic phase transition and its ultimate replacement with the collapsed tetragonal, nonmagnetic phase is similar to what has been observed for CaFe 2 As 2 under hydrostatic pressure. Transmission electron microscopy studies indicate that there is a temperature-dependent width of formation of CaFe 2 As 2 with a decreasing amount of excess Fe and As being soluble in the single crystal at lower annealing temperatures. For samples quenched from 960 • C there is a fine (of order 10 nm) semiuniform distribution of precipitate that can be associated with an average strain field, whereas for samples annealed at 400 • C the excess Fe and As form mesoscopic grains that induce little strain throughout the CaFe 2 As 2 lattice.