  We derive the anisotropic heat transport equation for rotating neutron stars
and the thermal equilibrium condition in a relativistic rotating axisymmetric
star is also derived through a simple variational argument. With a simple model
of neutron star, we model the propagation of heat pulses resulting from
transient energy releases inside the star. {\bf Such sudden energy release can
occur in pulsars during glitches.} Even in slow rotation limit ($\Omega\leq
1\times 10^{3}{s}^{-1}$), the results with rotational effects involved could be
noticeably different from those obtained with a spherically symmetric metric in
terms of the time scales and magnitudes of thermal afterglow. The effects of
gravitational lensing and frame dragging on the X-ray light curve pulsations
are also studied. The results we obtain indicate that the effect of rotation on
the light curve modulation is small, and the spacetime curvature effect
predominates. The metric components and rotational deformation on the stellar
structure are calculated by using Hartle-Thorne formalism. {\bf We have applied
our model to study the thermal response time scales of pulsars after glitches
and find that the centrifugal force produced by rotation can substantially
reduce the response time by a factor of three between non-rotating star and
rotating star with $\Omega \sim 900 s^{-1}$. The equation of state can also
affect the duration of response.
