A system for direct measurements of the magneto-caloric effect (MCE) exploits a rapid transport of a sample into or from magnetic field in permanent Halbach-type (1 T) or superconducting (4.7 T) magnets. Time dependence of induced changes of the sample temperature, ΔT(t), is detected directly by the differential Cu-Constantan-Cu micro-thermocouples with time steps of 300 ms. A sample placed inside an evacuated simple LN(2) cryostat is either totally isolated (adiabatic conditions) or partly connected with the copper sample holder (non-adiabatic conditions). The last arrangement (a model of the Brayton cycle) is used to simulate an application of MCE in refrigeration techniques. The relations describing ΔT(t) that allow an analysis of MCE of the studied materials are based on the general cooling law. The effect of the first-order magnetic transition on MCE of selected sample is also demonstrated by non-standard ΔT(t) curves measured in the last mentioned experimental arrangements.