Context. Ultraviolet (UV) bursts and Ellerman bombs (EBs) are transient brightenings observed in the low solar atmospheres of emerging flux regions. Magnetic reconnection is believed to be the main mechanism leading to formation of the two activities, which are usually formed far apart from each other. However, observations also led to the discovery of co-spatial and co-temporal EBs and UV bursts, and their formation mechanisms are still not clear. The multi-thermal components in these events, which span a large temperature range, challenge our understanding of magnetic reconnection and heating mechanisms in the partially ionized lower solar atmosphere. Aims. We studied magnetic reconnection between the emerging magnetic flux and back ground magnetic fields in the partially ionized and highly stratificated low solar atmosphere. We aim to explain the multi-thermal characteristics of UV bursts, and to find out whether EBs and UV bursts can be generated in the same reconnection process and how they are related with each other. We also aim to unearth the important small-scale physics in these events. Methods. We used the single-fluid magnetohydrodynamic (MHD) code NIRVANA to perform simulations. The background magnetic fields and emerging fields at the solar surface are reasonably strong. The initial plasma parameters are based on the C7 atmosphere model. We simulated cases with different resolutions, and included the effects of ambipolar diffusion, radiative cooling, and heat conduction. We analyzed the current density, plasma density, temperature, and velocity distributions in the main current sheet region, and synthesized the Sia IV emission spectrum. Results. After the current sheet with dense photosphere plasma emerges and reaches 0.5 Mm above the solar surface, plasmoid instability appears. The plasmoids collide and coalesce with each other, which causes the plasmas with different densities and temperatures to be mixed up in the turbulent reconnection region. Therefore, the hot plasmas corresponding to the UV emissions and colder plasmas corresponding to the emissions from other wavelengths can move together and occur at about the same height. In the meantime, the hot turbulent structures concentrate above 0.4 Mm, whereas the cool plasmas extend to much lower heights to the bottom of the current sheet. These phenomena are consistent with published observations in which UV bursts have a tendency to be located at greater heights close to corresponding EBs and all the EBs have partial overlap with corresponding UV bursts in space. The synthesized Sia IV line profiles are similar to that observed in UV bursts; the enhanced wing of the line profiles can extend to about 100 km s-1. The differences are significant among the numerical results with different resolutions, indicating that the realistic magnetic diffusivity is crucial to revealing the fine structures and realistic plasmas heating in these reconnection events. Our results also show that the reconnection heating contributed by ambipolar diffusion in the low chromosphere around the temperature minimum region is not efficient.