Even old (106 to 107 yr) pulsars within a few hundred parsecs of the Sun should give UV and optical fluxes via thermal radiation or radiation from relativistic particles. The surface temperature of a neutron star depends on its mass, radius, magnetic field, and internal composition (existence of pion condensate, superfluidity of nucléons, etc.). If the temperature exceeds ~2x104 K, the thermal radiation can be detected by the Hubble Space Telescope. An analysis of the results will allow one to study the thermal evolution and inner structure of neutron stars in order to obtain additional constraints on pulsar models.