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.Kinetic strange particle production models [1] imply that abundant strangeness is suggestive of the quark-gluon plasma (QGP). Even more specific information about the nature of the dense matter formed in relativistic nuclear collisions can be obtained considering strange quark and anti-quark clusters, since they are more sensitive to the environment from which they emerge [2]. Recently, the relative abundances of strange and multi-strange baryons and anti-baryons where studied experimentally [3,4]. It has been suggested that the observed particle abundances are in agreement with a picture of explosively disintegrating QGP fireball [6]. This postulate was supported by the observation that details of the produced particle multiplicity point to a high entropy primordial phase [7], and by a comprehensive analysis of the data which concluded that the hadron gas (HG) model cannot be brought into consistency with the experimental results [8].On the other hand, the alternative has been discussed [9,10,11] that the early experimental results [3], are compatible with the simplest possible scenario of an equilibrium, no flow, HG fireball being the particle source at which time it was noted that it is possible to distinguish the QGP and HG phases using the entropy content of the fireball [9]. We will show here that the HG alternative is not tenable anymore, given the larger and more precise set of experimental strange particle data [4,5] and that the modifications required * Unité associée au CNRS UA 280, Postal address: LPTHE Université PARIS 7, Tour 24, 5èét., 2 Place Jussieu, F-75251 CEDEX 05.