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In the presence of a minimal uncertainty in length, there exists a criticaltemperature above which the thermodynamics of a gas of radiation changesdrastically.  We find that the equilibrium temperature of a system composed of aSchwarzschild black hole surrounded by radiation is unaffected by thesemodifications. This is in agreement with works related to the robustness of theHawking evaporation. The only change the deformation introduces concerns thecritical volume at which the system ceases to be stable.  On the contrary, the evolution of the very early universe is sensitive to thenew behavior. We readdress the shortcomings of the standard big bangmodel(flatness, entropy and horizon problems) in this context, assuming aminimal coupling to general relativity. Although they are not solved, somequalitative differences set in.Comment: 10 pages revtex, 1 figur

Ultraviolet cutoff, black-hole-radiation equilibrium, and the big bang