The metabolism of all living organisms is dependent on temperature, and therefore, having a good method to predict temperature effects at a systems level is of importance. Here, we investigate the properties and robustness of a recently developed computational framework for enzyme and temperature constrained genome-scale models (etcGEM). The approach predicts the temperature dependence of an organism's metabolic network from thermodynamic properties of the metabolic enzymes, markedly expanding the scope and applicability of constraint-based metabolic modelling. We show that the existing Bayesian algorithm for fitting an etcGEM converges under a range of different priors and random seeds, yet the solutions differ both in parameter space and on a phenotypic level. We quantified the phenotypic consequences by studying the impact of different solutions on six metabolic network signature reactions. While two of these reactions showed little phenotype variation between the solutions, the remainder displayed huge variation in flux-carrying capacity. Furthermore, we made software improvements to reduce the running time of the compute-intensive Bayesian algorithm by a factor of 8.5. In addition, we develop an evolutionary algorithm as an alternative to the Bayesian parameter fitting algorithm. Our analysis shows that it also gives decent convergence, but it yields solutions with lower variability.