The field decay in neutron stars depends on the properties of matter i
n the core region. Joule heating accompanying the field decay can sign
ificantly influence the thermal history of neutron stars. The present
paper deals with the magnetic and thermal evolutions of neutron star w
ith the internal magnetic field. Two possible models of superdense mat
ter are considered, one with neutrons in normal state and the other wi
th neutron superfluidity. In both cases the internal field can decay o
n rather short time scale of the order of similar to 1 - 50 Myr. Joule
heating should essentially slow down neutron star cooling, particular
ly, at the late evolutionary stage. In the case of superfluid neutrons
an additional heating may be especially pronounced resulting even in
an increase of the surface temperature at some stages.