Dielectronic recombination (DR) experiments of highly charged ions not only provide essential atomic benchmark data for astrophysical and fusion plasma research but also serve as a stringent test for strong-field quantum electrodynamics (QED) effects, relativistic effects, and electron correlation effects. High-Intensity Heavy-Ion Accelerator Facility (HIAF), currently under construction at Huizhou, China, has a high-precision spectrometer ring (SRing) equipped with a 450 kV electron-cooler and an 80 kV ultracold electron-target. This advanced setup facilitates precise measurements of the DR process for highly charged ions across a broad range of center-of-mass energies, from meV to tens of keV. In this study, we employ molecular dynamics methods to simulate the electron beam temperature distribution of the ultracold electron-target at the SRing. The simulation results indicate that, following the designed adiabatic magnetic field and acceleration field treatment, the transverse and longitudinal electron beam temperature from the thermionic electron gun can be reduced from 100 meV to below 5 meV and 0.1 meV, respectively. Furthermore, we analyze the impact of this ultracold electron beam temperature on the resonance peaks and energy resolution in DR experiments. The resolution gain at the SRing electron-target is particularly pronounced at small electron-ion collision energies, which provides unique experimental conditions for the DR experiments. Using lithium-like ${ }_{54}^{129} \mathrm{Xe}^{51+}$ and ${ }_{92}^{238} U^{89+}$ ions as examples, we simulate the DR resonance spectrum at the SRing and compare them with the simulated results from the experimental cooler storage ring CSRe. The results reveal that the SRing experiments can resolve fine DR resonance structures with ultra-high energy resolution compared to those from the CSRe. This work lays the foundation for precise DR spectroscopy of highly charged ions at the SRing to stringent test of the strong-field QED effects and extract nuclear structure information.