Thermal afterglow caused by transient energy releases in neutron stars
could alter the X-ray pulse shape of pulsars by heating a portion of
the crust so that more thermal X-rays are emitted at a particular phas
e. We developed a method to look for such changes in X-ray pulsars. We
put a typical lower limit of 3.9 x 10(31) ergs s(-1) (1.4 x 10(35) er
gs in a 1 hr exposure) on the average excess X-ray luminosity required
to see thermal afterglow from ROSAT data of PSR 0656 + 14 consisting
of three separate observations lasting 3-5 hr. The lower limit obtaine
d allows us to constrain the glitch parameters and the equation of sta
te for neutron stars. In particular, a differentiation could be made b
etween the vortex unpinning model and the starquake model for pulsar g
litches if a search for thermal afterglow were performed contemporaneo
usly with glitch observations.