An experimental protocol which allows to perform conductance spectroscopy on organic molecules at low temperatures (T~30 K) has been developed. This extends the method of mechanically controlled break junctions which has recently demonstrated to be suitable to contact single molecules at room temperature. 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. Thus the comparability of experimental data with other measurements as well as with theoretical simulations is considerably improved.