We examine the thermal and dynamical response of a neutron star to a sudden perturbation of the inner crust temperature. During the star's evolution, starquakes and other processes may deposit $\gap 10^{42}$ ergs, causing significant internal heating and increased frictional coupling between the crust and the more rapidly rotating neutron superfluid the star is expected to contain. Through numerical simulation we study the propagation of the thermal wave created by the energy deposition, the induced motion of the interior superfluid, and the resulting spin evolution of the crust. We find that energy depositions of $\sim 10^{40}$ ergs produce gradual spin-ups above the timing noise level, while larger energy depositions produce sudden spin jumps resembling pulsar glitches. For a star with a temperature in the observed range of the Vela pulsar, an energy deposition of $\sim 10^{42}$ ergs produces a large spin-up taking place over minutes, similar to the Vela ``Christmas'' glitch. Comparable energy deposition in a younger and hotter ``Crab-like'' star produces a smaller spin-up taking place over $\sim 1$ day, similar to that seen during the partially time-resolved Crab glitch of 1989.

21 pages plus 17 figures, uuencode compressed Postscript. Accepted for publication in the Astrophysical Journal