  Considering Joule heating caused by the dissipation of the magnetic field in
the neutron star crust to be an efficient mechanism in maintaining a relatively
high surface temperature in very old neutron stars, the role of general
relativity is investigated. It is found that, although the effect of space-time
curvature produced by the intense gravitational field of the star slows down
the decay rate of the magnetic field, modification of the initial magnetic
field configuration and the initial field strength by the space-time curvature
results in increasing the rate of Joule heating. Hence the space-time curvature
supports Joule heating in maintaining a relatively high surface temperature
which is consistent with the bservational detection.
