This work presents a study of the thermal evaporation and stability of pyrene (C16H10)n clusters. Thermal evaporation rates of positively charged mass-selected clusters are measured for sizes in the range n = 3-40 pyrene units. The experimental setup consists of a gas aggregation source, a thermalization chamber, and a time of flight mass spectrometer. A microcanonical Phase Space Theory (PST) simulation is used to determine the dissociation energies of pyrene clusters by fitting the experimental breakdown curves. Calculations using the Density Functional based Tight Binding combined with a Configuration Interaction (CI-DFTB) model and a hierarchical optimization scheme are also performed in the range n = 2-7 to determine the harmonic frequencies and a theoretical estimation of the dissociation energies. The frequencies are used in the calculations of the density of states needed in the PST simulations, assuming an extrapolation scheme for clusters larger than 7 units. Using the PST model with a minimal set of adjustable parameters, we obtain good fits of the experimental breakdown curves over the full studied size range. The approximations inherent to the PST simulation and the influence of the used parameters are carefully estimated. The derived dissociation energies show significant variations over the studied size range. Compared with neutral clusters, significantly higher values of the dissociation energies are obtained for the smaller sizes and attributed to charge resonance in line with CI-DFTB calculations.