In this research work, a Cu-based HTSMA (high temperature shape memory alloy) with a new quaternary Cu-21.52Al-3.49Fe-1.95Mn (at%) composition was produced by arc melting and the samples cut from this cast-ingot alloy were aged all at 250 degrees C thermally for 1 h and then quenched or cooled in several different coolant media. In order to determine the effects of the quenching/cooling media on the characteristic martensitic transformation temperatures, thermodynamic parameters and structural features of the HTSMA alloy the thermal analyses were executed by differential scanning calorimetry (DSC) and differential thermal analysis (DTA) measurements at different heating/cooling rates for every sample quenched/cooled in different medium. The characteristic direct and reverse martensitic phase transitions occured at high temperatures (above 100 degrees C) were appeared on the all heating/cooling DSC curves. The DSC analyses also showed that the highest transformation temperatures were determined for the sample quenched in boiling water and the lowest ones for the sample that quenched in icedbrine water. Among the coolant quenching media, the liquid nitrogen and boiling water with having the fastest coolant effects on the aged hotter alloy were found that they led alloy to have the least entalphy and entropy change amounts during martensitic phase transformations of this aged alloy. Also these fastest coolant media caused the formations of finest and neatest martensite structures in the alloy with the lowest degree of atomic orders. The X-ray analyses were made at room conditions to determine the structural features, the diffraction planes and their corresponding phases of the aged CuAlFeMn alloy samples. For all of the samples, the prevailing martensite planes were observed as the peaks resulted from beta 1'(18R) planes and the largest crystallite size was determined for the alloy sample quenched in liquid nitrogen which implied that the sample became to have the finest single monolith crystallite with the lowest degree of atomic order, this came out just like the indications and results of DSC analyses. Furthermore, it can be said that using liquid nitrogen or boiling water as a coolant quenching medium after heat treatments on HTSMAs can give better results than using traditional iced-brine water quenching medium. From all results, it is found that the type of quenching medium causes significant distinct effects on the heat treated CuAlFeMn HTSMA, so the different requirements demanded in SMA related applications can be afforded by choosing the appropriate aging and quenching method.