The atomic scale dynamics of halide perovskites have a direct impact not only on their thermal stability but their optoelectronic properties. Progress in machine learned potentials has only recently enabled modeling the finite temperature behavior of these material using fully atomistic methods with near first-principles accuracy. Here, we systematically analyze the impact of heating and cooling rate, simulation size, model uncertainty, and the role of the underlying exchange-correlation functional on the phase behavior of CsPbX3 with X=Cl, Br, and I, including both the perovskite and the delta-phases. We show that rates below approximately 30 K/ns and system sizes of at least a few ten thousand atoms are indicated to achieve convergence with regard to these parameters. By controlling these factors and constructing models that are specific for different exchange-correlation functionals we then show that the semi-local functionals considered in this work (SCAN, vdW-DF-cx, PBEsol, and PBE) systematically underestimate the transition temperatures separating the perovskite phases while overestimating the lattice parameters. Among the considered functionals the vdW-DF-cx functional yields the closest agreement with experiment, followed by SCAN, PBEsol, and PBE. Our work provides guidelines for the systematic analysis of dynamics and phase transitions in inorganic halide perovskites and similar systems. It also serves as a benchmark for the further development of machine-learned potentials as well as exchange-correlation functionals.