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The magnetic and thermal evolution of neutron stars is a very complex processwith many nonlinear interactions. For a decent understanding of neutron starphysics, these evolutions cannot be considered isolated. A brief overview ispresented, which describes the main magnetothermal interactions that determinethe fate of both isolated neutron stars and accreting ones. Special attentionis devoted to the interplay of thermal and magnetic evolution at the polar capof radio pulsars. There, a strong meridional temperature gradient is maintainedover the lifetime of radio pulsars. It may be strong enough to drivethermoelectric magnetic field creation which perpetuate a toroidal magneticfield around the polar cap rim. Such a local field component may amplify andcurve the poloidal surface field at the cap, forming a strong and small scalemagnetic field as required for the radio emission of pulsars

Magnetothermal Evolution of Neutron Stars with Emphasis to Radio Pulsars