The linear temporal stability of the fully developed pulsatile flow in a torus with high curvature is investigated using Floquet theory. The baseflow is computed via a Newton-Raphson iteration in frequency space to obtain basic states at supercritical Reynolds numbers in the steady case for two curvatures, δ=0.1 and 0.3, exhibiting structurally different linear instabilities for the steady flow. The addition of a pulsatile component is found to be overall stabilizing over a wide range of pulsation amplitudes, in particular for high values of curvature. The pulsatile flows are found to be at most transiently stable with large intracyclic growth rate variations even at small pulsation amplitudes. While these growth rates are likely insufficient to trigger an abrupt transition at the parameters in this work, the trends indicate that this is indeed likely for higher pulsation amplitudes, similar to pulsatile flow in straight pipes. At the edge of the considered parameter range, subharmonic eigenvalue orbits in the local spectrum of the time-periodic operator, recently found in pulsating channel flow, have been confirmed also for pulsatile flow in toroidal pipes, underlining the generality of this phenomenon.