The expansion of a spherical hot-spot within an infinite D-T medium is examined and the production of thermonuclear energy is calculated through the numerical solution of the plasma-fluid equations in a number of cases. Two kinds of hot-spots are considered in which the ions are initially either hot (ionic H-S) or cold (electronic H-S). The conditions for a positive energy balance and the ignition of a thermonuclear reaction wave are derived. At solid-state density a pulsed fusion reactor requires an energy of 103–104 MJ. Extensions are made to plane and cylindrical H-S and the expansion of a spherical H-S in vacuum. The thermonuclear output is not improved by progressive H-S heating or a decrease in thermal conductivity in a transverse magnetic field.