The impact of disulfide bonds on protein stability goes beyond simple equilibrium thermodynamics effects associated with the conformational entropy of the unfolded state. Indeed, disulfide crosslinks may play a role in the prevention of dysfunctional association and strongly affect the rates of irreversible enzyme inactivation, highly relevant in biotechnological applications. While these kinetic-stability effects remain poorly understood, by analogy with proposed mechanisms for processes of protein aggregation and fibrillogenesis, we propose that they may be determined by the properties of sparsely-populated, partially-unfolded intermediates. Here we report the successful design, on the basis of high temperature molecular-dynamics simulations, of six thermodynamically and kinetically stabilized variants of phytase from Citrobacter braakii (a biotechnologically important enzyme) with one, two or three engineered disulfides. Activity measurements and 3D crystal structure determination demonstrate that the engineered crosslinks do not cause dramatic alterations in the native structure. The inactivation kinetics for all the variants displays a strongly non-Arrhenius temperature dependence, with the time-scale for the irreversible denaturation process reaching a minimum at a given temperature within the range of the denaturation transition. We show this striking feature to be a signature of a key role played by a partially unfolded, intermediate state/ensemble. Energetic and mutational analyses confirm that the intermediate is highly unfolded (akin to a proposed critical intermediate in the misfolding of the prion protein), a result that explains the observed kinetic stabilization. Our results provide a rationale for the kinetic-stability consequences of disulfide-crosslink engineering and an experimental methodology to arrive at energetic/structural descriptions of the sparsely populated and elusive intermediates that play key roles in irreversible protein denaturation.