In this report, we present findings of systematic research on NiCoMnAl alloys, with the purpose of acquiring a higher thermal transformation arrest temperature (TA). By systematic research, TA in the NiCoMnAl alloy systems was raised up to 190 K, compared to the highest TA of 130 K in NiCoMnIn. For a selected alloy of Ni40Co10Mn33Al17, magnetization measurements were performed under a pulsed high magnetic field, and the critical magnetic field-temperature phase diagram was determined. The magnetic phase diagram for Ni50-xCoxMn50-yAly was also established. Moreover, from the discussion that the formerly called “kinetic arrest phenomenon” has both thermodynamic and kinetic factors, we suggest a terminology change to the “thermal transformation arrest phenomenon”.