In an effort to understand the impact of nanostructuring on the magnetocaloric effect, we have grown and studied gadolinium in MgO/W(50 $textrm{AA}$)/[Gd(400 $textrm{AA}$)/W(50 $textrm{AA}$)]$_8$ heterostructures. The entropy change associated with the second order magnetic phase transition was determined from the isothermal magnetization for numerous temperatures and the appropriate Maxwell relation. The entropy change peaks at a temperature of 284 K with a value of approximately 3.4 J/kg-K for a 0-30 kOe field change; the full width at half max of the entropy change peak is about 70 K, which is significantly wider than that of bulk Gd under similar conditions. The relative cooling power of this nanoscale system is about 240 J/kg, somewhat lower than that of bulk Gd (410 J/kg). An iterative Kovel-Fisher method was used to determine the critical exponents governing the phase transition to be $beta=0.51$, and $gamma=1.75$. Along with a suppressed Curie temperature relative to the bulk, the fact that the convergent value of $gamma$ is that predicted by the 2-D Ising model may suggest that finite size effects play an important role in this system. Together, these observations suggest that nanostructuring may be a promising route to tailoring the magnetocaloric response of materials.