We present an experimental protocol which allows to perform conductance spectroscopy on single organic molecules at low temperatures (T » 30K) . The conductance data obtained at low-T with a conjugated sample molecule show a highly improved data quality with a higher stability, narrower linewidth and substantially reduced noise compared to room-temperature (RT) data . For the RT measurements a rather broad range of sample-to-sample fluctuations was attributed to different microscopic contact realisations. The smaller number of variations in the recorded low-T spectra might indicate that here energetically favourable configurations occure more frequently. Thus the comparability of experimental data with other experiments as well as with theoretical simulations is considerably improved.