The Scalable LIquid Metal–cooled small Modular (SLIMM) reactor generates 10 to 100 MW(thermal) for extended periods without refueling. With the aid of an in-vessel chimney and a Na/Na helically coiled tubes heat exchanger (HEX) in the downcomer, natural circulation of in-vessel liquid sodium cools the SLIMM reactor core during nominal operation and after shutdown. With an unlikely malfunction of the Na/Na HEX, natural circulation of ambient air along the outer surface of the guard vessel wall maintains in-vessel natural circulation of liquid sodium and passively removes the decay heat after reactor shutdown. This paper performs three-dimensional computational fluid dynamics and thermal-hydraulic analyses to obtain preliminary estimates of the rate of decay heat removal by ambient air in case of a malfunction of the in-vessel Na/Na HEX and investigates the effect of using longitudinal metal fins along the guard vessel outer surface. The analyses calculate the contributions of natural convection and thermal radiation to the rate of decay heat removal by ambient air. For the same sodium temperatures in the reactor vessel downcomer as during steady-state nominal operation at 100 MW(thermal), the decay heat removal rate by ambient air without metal fins is ~1.0 MW(thermal), increasing by 26% to 1.26 MW(thermal) with metal fins. The contributions of natural convection and thermal radiation to the rate of decay heat removal are 58% and 42% without metal fins and 70% and 30% with metal fins, respectively. Extending the metal fins an additional 5 m and doubling the axial thermal conductivity increase the rate of the decay heat removal only slightly, to 1.28 MW(thermal).