We reconsider thermal conditions of the central fireball presumed to be the source of abundantly produced strange (anti-)baryons in S -> W collisions at 200 GeV A. We show that it is possible to completely fix the freeze-out temperature of strange particles in terms of the central rapidity kaon to Lambda particle abundance ratio at fixed, high transverse mass using a non-equilibrium hadronization model and the measured quark fugacities.