An investigation of the sympathetic cooling method for the studies of large ultra-cold molecular ions in a quadrupole ion trap has been conducted.Molecular dynamics simulations are performed to study the rf heating mechanisms in the ion trap. The dependence of rf heating rates on the ion temperature, trapping parameters, and the number of ions is obtained. New rf heating mechanism affecting ultra-cold ion clouds exposed to laser radiation is described.The saturation spectroscopy setup of the hyperfine spectra of the molecular iodine has been built to provide an accurate frequency reference for the laser wavelength. This reference is used to obtain the fluorescence lineshapes of the laser cooled Mg$^+$ ions under different trapping conditions.The ion temperatures are deduced from the measurements, and the influence of the rf heating rates on the fluorescence lineshapes is also discussed. Cooling of the heavy ($m=720$a.u.) fullerene ions to under 10K by the means of the sympathetic cooling by the Mg$^+$ ions($m=24$a.u.) is demonstrated. The single-photon imaging system has been developed and used to obtain the images of the Mg$^+$ ion crystal structures at mK temperatures.
