Following the previous work by our group, the operation of the helium-filled counter has been studied more in detail at liquid-helium (∼ 5 K), liquid-nitrogen (77 K) and room (295 K) temperatures. The collimated σ-ray beam from a 210Po source, which is installed inside the counter, has made it possible to measure the gas gain M from the ionization-chamber region with M = ∼1. The operation of the helium-filled counter is rather unstable at 77 and 295 K; when the applied voltage is increased, the gas gain steeply rises up to 103 and the pulse rise time becomes longer than 200 μm. On the other hand, the counter works stably at 5 K, although available gas gains are comparatively small, i.e., at most 170. The slope of gas gain at 5 K is more gentle than that at 77 or 295 K and the pulse rise time does not change (∼ 2 μs) so much in the wide range of applied voltage. Measured results for gas gain and pulse rise time are reported in this paper.The favourable operation at 5 K is not only due to the absence of impurity in helium gas but also to the suppression of electron emission from the cathode. This new feature of the proportional-counter operation at a very low temperature is also discussed from the standpoint of atomic processes in helium gas.