  We show that the soft X-ray spectra and light curves observed with the ROSAT
and EUVE from the closest known millisecond pulsar J0437--4715 can be
interpreted as thermal radiation from two hot polar caps whose emitting layers
(atmospheres) are comprised of hydrogen. The simplest model yields a uniform
temperature of $(0.8-0.9)\times 10^6 K$ within a cap radius of $0.7-0.9 km$.
The spectral fits indicate that the temperature may be nonuniformly distributed
along the cap surface. The distribution can be approximated by a central core
heated up to $(1-2)\times 10^6 K$ within a radius of $0.2-0.4 km$, surrounded
by a colder rim with temperatures $(3-5)\times 10^5 K$ extending out to $2-6
km$. The polar cap interpretation implies low column densities, $(1-3)\times
10^{19} cm^{-2}$, and a high degree of ionization, $> 20$%, of the interstellar
hydrogen towards the pulsar. The inferred bolometric luminosity of the polar
caps, $(1.0-1.6)\times 10^{30} erg s^{-1}$, is in excellent agreement with the
predictions of the slot-gap model of radio pulsars developed by Arons and his
coworkers. Similar polar cap radiation should be emitted by other millisecond
pulsars, although in some of them (e.~g., PSR B1821--24) the soft X-ray flux is
dominated by the nonthermal radiation from pulsar magnetospheres.
