  The magnetic and thermal evolution of neutron stars is a very complex process
with many nonlinear interactions. For a decent understanding of neutron star
physics, these evolutions cannot be considered isolated. A brief overview is
presented, which describes the main magnetothermal interactions that determine
the fate of both isolated neutron stars and accreting ones. Special attention
is devoted to the interplay of thermal and magnetic evolution at the polar cap
of radio pulsars. There, a strong meridional temperature gradient is maintained
over the lifetime of radio pulsars. It may be strong enough to drive
thermoelectric magnetic field creation which perpetuate a toroidal magnetic
field around the polar cap rim. Such a local field component may amplify and
curve the poloidal surface field at the cap, forming a strong and small scale
magnetic field as required for the radio emission of pulsars
