  Isolated ideal neutron stars (NS) of age $>10^9$ yrs exhaust thermal and
rotational energies and cool down to temperatures below $\mathcal{O}(100)$ K.
Accretion of particle dark matter (DM) by such NS can heat them up through
kinetic and annihilation processes. This increases the NS surface temperature
to a maximum of $\sim 2550$ K in the best case scenario. The maximum accretion
rate depends on the DM ambient density and velocity dispersion, and on the NS
equation of state and their velocity distributions. Upon scanning over these
variables, we find that the effective surface temperature varies at most by
$\sim 40\%$. Black body spectrum of such warm NS peak at near infrared
wavelengths with magnitudes in the range potentially detectable by the James
Webb Space Telescope (JWST). Using the JWST exposure time calculator, we
demonstrate that NS with surface temperatures $\gtrsim 2400$ K, located at a
distance of 10\,pc can be detected through the F150W2 (F322W2) filters of the
NIRCAM instrument at SNR\,$\gtrsim 10$ (5) within 24 hours of exposure time.
Independently of DM, an observation of NS with surface temperatures $\gtrsim
2500$ K will be a formative step towards testing the minimal cooling paradigm
during late evolutionary stages.
