We have measured the temperature dependence of positron lifetimes in a ${\mathrm{Pb}}_{96.1}$${\mathrm{Cd}}_{3.9}$ alloy having a dislocation density large enough to significantly affect the ${e}^{+}{e}^{\ensuremath{-}}$ annihilation spectra. These spectra were resolved into two unconstrained lifetimes in addition to a sourceterm lifetime. The longer of the two lifetimes, which is attributed to positrons localized by traps associated with dislocations, decreases with increasing sample temperature $T$ at about 0.1 psec ${\mathrm{K}}^{\ensuremath{-}1}$ for $90\ensuremath{\le}T\ensuremath{\le}300$ K. These data represent the first reported observation of a temperature-dependent lifetime of positrons localized at dislocation traps. It is proposed that the temperature dependence is principally due to atoms penetrating deeper into the traps as $T$ is raised. We suggest that these atomic incursions also effect a negative contribution to the slope of the line-shape parameter $S(T)$. Analysis of the data in terms of the two-state trapping model reveals (i) that both the trapping rate per unit dislocation density and the probability of annihilation occurring at the dislocation traps for constant dislocation density are weakly temperature dependent, and (ii) that during recovery anneals the total trapping rate decreases markedly, whereas little change is exhibited by the lifetime of the trapped positron.