  We investigate the luminosity and cooling of highly magnetized white dwarfs
where cooling occurs by the diffusion of photons. We solve the magnetostatic
equilibrium and photon diffusion equations to obtain the temperature and
density profiles in the surface layers of these white dwarfs. With increase in
field strength, the degenerate core shrinks in volume with a simultaneous
increase in the core temperature. For a given white dwarf age and for a fixed
interface radius or temperature, the luminosity decreases significantly from
$\sim 10^{-6}\, L_{\odot}$ to $10^{-9}\, L_{\odot}$ as the field strength
increases from $\sim 10^9$ to $10^{12}\,$G in the surface layers. This is
remarkable as it argues that magnetized white dwarfs can remain practically
hidden in an observed H--R diagram. We also find that the cooling rates for
these highly magnetized white dwarfs are suppressed significantly.
