Caloric cooling enlisting solid-state refrigerants is potentially a promising eco-friendly alternative to conventional cooling based on vapor compression. The most common refrigerant materials for elastocaloric cooling to date are Ni-Ti based superelastic shape memory alloys. Here, we have explored tuning the operation temperature range of Ni50.8Ti49.2 for elastocaloric cooling. In particular, we have studied the effect of thermal treatments (a.k.a. aging) on the transformation temperature, superelasticity, and elastocaloric effects of Ni50.8Ti49.2 shape memory alloy tubes. The isothermal compressive test revealed that the residual strain of thermally-treated Ni-Ti tubes at room temperature approaches zero as aging time is increased. Short-time aging treatment at 400 ◦C resulted in good superelasticity and elastocaloric cooling performance with a large tunable austenite finish (Af) temperature range of 24.7 ◦C, as determined from the Af temperature of the samples that were aged 5–120 min. The main reason of the property change is the formation of a different amount of Ni4Ti3 precipitates in the NiTi matrix. Our findings show that it is possible to tailor the Af temperature range for development of cascade elastocaloric cooling systems by thermally treating a starting single composition Ni-Ti alloy.