Hysteresis loop measurements of superconducting polycrystalline samples of Tl-2223 were carried out at various temperatures. Using the magnetization remanence (M_R) as measurement of the maximum vortex flux pinning at each temperature, our results reveal that the vortex flux pinning forces show two distinct behaviours of M_R with temperature, a linear behaviour with t at high temperatures and an exponential behaviour with t^β at low temperatures, where t = (1-T/T_c) and β is constant of order 8. The effect of γ-irradiation shows six-fold enhancement in the vortex pinning over all temperatures up to T_c. This increase in the pinning forces is attributed to the induced defects introduced by the γ-irradiation. The same enhancement in the pinning forces at all temperatures implies constant defects induced by γ-irradiation.