The Ellerman Bomb (EBs) is a kind of small scale reconnection events, which are ubiquitously formed in the upper photosphere or the lower chromosphere. The low temperature ($<10,000$\,K) and high density ($\sim 10^{19}-10^{22}$) plasma there make the magnetic reconnection process strongly influenced by the partially ionized effects and the radiative cooling. This work studied the high $\beta$ magnetic reconnection near the solar temperature minimum region (TMR) based on high-resolution 2.5D magnetohydrodynamics (MHD) simulations. The time-dependent ionization degree of hydrogen and helium are included to realize more realistic diffusivities, viscosity and radiative cooling in simulations. Numerical results show that the reconnection rate is smaller than 0.01 and decreases with time during the early quasi-steady stage, then sharply increases to a value above 0.05 in the later stage as the tearing model (plasmoid) instability takes place. Both the large value of $\eta_{en}$ (magnetic diffusion caused by the electron-neutral collision) and the plasmoid instability contribute to the fast magnetic reconnection in the EB-like event. The interactions and the coalescence of plasmoids strongly enhance the local compression heating effect, which becomes the dominant mechanism for heating in EBs after plasmoid instability appears. However, the Joule heating contributed by $\eta_{en}$ can play a major role to heat plasmas when the magnetic reconnection in EBs is during the quasi-steady stage with smaller temperature increases. The results also show that the radiative cooling effect suppresses the temperature increase to a reasonable range, increases the reconnection rate and the generation of thermal energy.
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