Measurements of the thermal conductivity of helium and hydrogen are performed using the transient short-hot-wire method. The short hot wire is made of platinum and has a diameter of about 10 mu m and a length of about 15 mm. It is attached by spot welding to platinum terminals with a diameter of 1.5 mm. The probe is inserted into the sample vessel that has a volume of 35 cm(3) and an inner diameter of 30 mm. The thermal conductivity is evaluated by comparing a numerical solution of the heat conduction in and around the short wire with the experimentally obtained temperature rise of the wire. The measured thermal conductivities show good reproducibility. Also, the measured thermal conductivities agree with the reference equations within a deviation of. +/- 1%.