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The two-dimensional ferromagnetic Kondo model with classical core spins is studied via unbiased Monte Carlo simulations for a hole doping up to x = 12.5%. A canonical algorithm for finite temperatures is developed. We show that, with realistic parameters for the manganites and at low temperatures, the double-exchange mechanism does not lead to phase separation on a two-dimensional lattice but rather stabilizes individual ferromagnetic polarons for this doping range. A detailed analysis of unbiased Monte Carlo results reveals that the polarons can be treated as independent particles for these hole concentrations. It is found that a simple polaron model describes the physics of the ferromagnetic Kondo model amazingly well. The ferromagnetic polaron picture provides an obvious explanation for the pseudogap in the one-particle spectral function Ak(ω) observed in the ferromagnetic Kondo model.