Magnetic reconnection is the most likely mechanism responsible for the high temperature events that are observed in strongly magnetized locations around the temperature minimum in the low solar chromosphere. This work improves upon our previous work [Ni et al., Astrophys. J. 852, 95 (2018)] by using a more realistic radiative cooling model computed from the OPACITY project and the CHIANTI database. We find that the rate of ionization of the neutral component of the plasma is still faster than recombination within the current sheet region. For low beta plasmas, the ionized and neutral fluid flows are well-coupled throughout the reconnection region resembling the single-fluid Sweet-Parker model dynamics. Decoupling of the ion and neutral inflows appears in the higher beta case with beta(0) = 1.46, which leads to a reconnection rate about three times faster than the rate predicted by the Sweet-Parker model. In all cases, the plasma temperature increases with time inside the current sheet, and the maximum value is above 2 x 10(4) K when the reconnection magnetic field strength is greater than 500 G. While the more realistic radiative cooling model does not result in qualitative changes of the characteristics of magnetic reconnection, it is necessary for studying the variations of the plasma temperature and ionization fraction inside current sheets in strongly magnetized regions of the low solar atmosphere. It is also important for studying energy conversion during the magnetic reconnection process when the hydrogen-dominated plasma approaches full ionization. Published by AIP Publishing.