The governing equations of thermal-hydraulic flows exhibit numerical stiffness as a consequence of significant differences in the physical behavior of the phase constituents and the presence of stiff source terms. Computational methods to cope with these issues are evaluated in this work based on a two-fluid model. To circumvent the stringent time-step restrictions of explicit schemes imposed by stability limits, a parallel implicit Newton-Krylov-Schwarz (NKS) approach is investigated. However, the ability to take a much larger time step is not tantamount to low computational cost, as implicit methods applied to multiphase flows do require the solution of a sparse, linear system of equations, which increases the memory requirements and computational cost per iteration. Parallel implementations of implicit schemes are also more difficult to achieve than those of explicit methods. Consequently, an assessment of the implicit method is required to guide the choice of optimal parameters for convergence acceleration, which in many instances is problem dependent. Previous studies on the computational cost of implicit vs. explicit methods for the same solution accuracy have not been conclusive. This work aims to expand the body of research on this issue by studying the properties of the parallel implicit NKS algorithm for a range of relevant thermal-hydraulic benchmark problems.