Thermal rate coefficients for forming H{sub 2} via associative detachment in H{sup -} + H collisions were determined using the combination of a 22-pole ion trap (22PT) with a skimmed effusive beam of atomic hydrogen penetrating the ion cloud. The temperature of both reactants have been varied independently (ion trap: T{sub 22PT} = 10-150 K, neutral beam accommodator T{sub ACC} = 10, 50, 120 K). Using various combinations, the temperature range between 10 and 135 K has been accessed for the first time experimentally. The effective number density of H (typically some 10{sup 8} cm{sup -3}) is determined in situ via chemical probing with CO{sup +}{sub 2} ions. With decreasing temperature, the measured thermal rate coefficients decrease slowly from 5.5 Multiplication-Sign 10{sup -9} cm{sup 3} s{sup -1} at 135 K to 4.1 Multiplication-Sign 10{sup -9} cm{sup 3} s{sup -1} at 10 K. The relative error is 10%, while the absolute values may deviate systematically by up to 40%, due to uncertainties in the calibration reaction. Significant improvements of the versatile and sensitive experiment are possible, e.g., by using electron transfer from H to D{sup +} as calibration standard.