We report non-detections of the $sim 3times 10^8$ yr old, slow, isolated, rotation-powered pulsar PSR J2144$-$3933 in observations with the Hubble Space Telescope in one optical band (F475X) and two far-ultraviolet bands (F125LP and F140LP), yielding upper bounds $F_{rm F475X}< 22.7$ nJy, $F_{rm F125LP}< 5.9$ nJy, $F_{rm F140LP}< 19.5$ nJy, at the pivot wavelengths 4940 AA, 1438 AA and 1528 AA, respectively. Assuming a blackbody spectrum, we deduce a conservative upper bound on the surface (unredshifted) temperature of the pulsar of $T<42,000$ K. This makes PSR~J2144--3933 the coldest known neutron star, allowing us to study thermal evolution models of old neutron stars. This temperature is consistent with models with either direct or modified Urca reactions including rotochemical heating, and, considering frictional heating from the motion of neutron vortex lines, it puts an upper bound on the excess angular momentum in the neutron superfluid, $J<10^{44},mathrm{erg,s}$.
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