The behavior of the Crab pulsar following the 1969 and 1975 glitches and the postglich behavior of the old pulsar PSR 0525 + 21 are explained as resulting from internal torques due to the thermal creep of vortex lines in pinned superfluid regions. An overview of vortex creep theory is first given, and the immediate postglitch behavior of the Crab pulsar is calculated and compared with observation. The persistent shift in the spin-down rate observed for the Crab pulsar following the 1975 glitch is considered, and the internal and surface temperatures of this pulsar are deduced. The postglich behavior expected for very old pulsars is examined, showing that PSR 0525 + 21 falls into this category. It is concluded that the behavior of the Crab pulsar following both glitches can be characterized by the same two pinning regions. A comparison of the internal temperature for the Crab and Vela pulsars provides a significant constraint on the cooling of neutron stars.