Finite difference numerical methods are available for the computation of unsteady non-isothermal flows with possibly strong buoyancy effects or head loss terms. The algorithm uses either velocity-pressure or velocity-stream-function formulations. The treatment of advective terms involves the method of characteristics. Arbitrary non-orthogonal curvilinear grids may be used, and turbulence is modeled by means of a k-ϵ eddy viscosity model. Two examples of application to liquid-metal fast breeder reactor thermal analysis are: 1. hot plenum flow in a pool-type vessel during flow and thermal transients, 2. unsteady flow in a pipe resulting from an inlet temperature change with a very low flow rate. For both cases, comparisons with experimental studies and applications to real reactors are shown.