Exchange interactions and Curie temperatures of CoFeCrZ (Z=P, As, Sb, Ge) quaternary Heusler alloys are studied by using the spin-polarized relativistic Korringa-Kohn-Rostoker method. Electronic calculations show that the CoFeCrZ alloys apart from CoFeCrP are ferromagnetic half-metals, and their integer magnetic moments obey the Slater-Pauling rule. It is confirmed that the calculated Curie temperatures are evidently higher than room temperature. Further, we discuss the dependency of magnetic moments and Curie temperatures with respect to lattice constants. A smaller Gilbert damping parameters imply that these alloys have lower energy loss in spintronics applications. In addition, the thermoelectric properties of CoFeCrZ in both spin channels are calculated based on the BoltzTrap code. Results indicate that the Seebeck coefficients of CoFeCrZ (Z=As, Sb, Ge) are remarkably higher than 1000 mu V/K. Overall, we think that the CoFeCrAs, CoFeCrSb and CoFeCrGe alloys are promising candidates in future spintronic and thermoelectric applications.