Dielectronic recombination (DR) is one of the dominant electron-ion recombination mechanisms for most highly charged ions (HCIs) in cosmic plasmas, and thus, it determines the charge state distribution and ionization balance therein. To reliably interpret spectra from cosmic sources and model the astrophysical plasmas, precise DR rate coefficients are required to build up an accurate understanding of the ionization balance of the sources. The storage rings CSRm and CSRe at the Heavy-Ion Research Facility in Lanzhou (HIRFL) are both equipped with electron cooling devices, which provide an excellent experimental platform for electron-ion collision studies for HCIs. Here, the status of the DR experiments at the HIRFL-CSR is outlined, and the DR measurements with Na-like Kr25+ ions at the CSRm and CSRe are taken as examples. In addition, the plasma recombination rate coefficients for Ar12+, 14+, Ca14+, 16+, 17+, Ni19+, and Kr25+ ions obtained at the HIRFL-CSR are provided. All the data presented in this paper are openly available at https://www.scidb.cn/anonymous/UUpuSWZx.