The minimum mass of a neutron star is actually about 0.2 solar masses and has nothing to do with the Chandrasekhar limit (see this Physics SE answer). It seems unlikely however that there is any astrophysical channel to produce such neutron stars.
Several neutron stars have precisely measured masses that are smaller than 1.44 solar masses. The smallest is currently about 1.17 solar masses (Martinez et al. 2015). Note that more massive neutron stars may actually have smaller radii. It depends on the uncertain relationship between pressure and density.
The plot below shows theoretical relationships between masses and radii of neutron stars. The measured mass range for neutron stars is 1.17-2.1 solar masses, so you could estimate the smallest possible radius from your favourite model curve. For the "softest" equations of state (labelled "SQM1, where quark matter develops at the neutron star core), the smallest radius for a 1.17 solar mass neutron star is about 8.5 km.
Actually measuring the radii of neutron stars is incredibly difficult. The "measurements" that exist are rather indirect inferences and have large uncertainties.
There is however a fundamental limit in General Relativity, that is larger than the Schwarzschild radius, for the minimum radius of an object at a given mass. This "Buchdahl limit" is 9/8 of the Schwarzschild radius (shown in the picture as a forbidden region, labelled "GR"). It does not matter what type of pressure support is provided, a spherically symmetric object will collapse to a black hole if smaller than that.
For realistic relationships between pressure and density, then the true limit is a bit bigger than the Buchdahl limit - perhaps 1.2 to 1.3 times the Schwarzschild radius (represented by the grey forbidden region labelled "causality"). This is around 5 km, for neutron stars with the smallest measured masses, so presumably those neutron stars are bigger than that.
Rapid rotation could change some of these considerations, but the measured rotation rates of pulsars are too slow to have much effect.
I think the reason for the strange, small radius values you see (especially in Wikipedia, which does not have much quality control - always look at the original sources) is that it is a "fitting parameter" and represents the size of the emitting region and not necessarily the radius of the neutron star.
Finally, the surface temperature of a neutron star does not directly depend on its radius. Neutron stars start their lives very hot and cool down with time. To first order, the surface temperature of a neutron star would depend on its age. It could also depend on the rate at which it was accreting material from the interstellar medium (or a companion) or perhaps even its initial magnetic field strength.