Thermally-activated flux flow (TAFF) resistivity above the irreversibility field Bi is reported for two different c-axis textured MgB2 superconducting films. Transport measurements at different perpendicular magnetic fields 0<B<9 T and temperatures from 5 to 40 K reveal TAFF Ohmic resistivity ρ(T,B) for B>Bi described by the Arrhenius law, ρ=ρ0 exp(-U∕T) with the quadratic field dependence of the activation energy, U(B,T)=U0(T)[1−B∕Bc2(T)]2. Our transport measurements on bulk MgB2 ceramic samples also show the TAFF behavior, but do not show the quadratic field dependence of U(T,B). We explain our data in terms of thermally-activated drift of pre-existing quenched dislocations in the vortex lattice. Our results indicate that thermal fluctuations can be essential in determining the irreversibility field in MgB2 though to a much lesser extent than in high-temperature superconductors.