Zhang Chong-Hong group has found that pre-irradiation of helium ions at low temperature with very low dose could effectively suppress helium bubble growth in materials. This experimental result lacks theoretical explanation. In this paper, we use Monte Carlo simulation to study the effects of different temperature modes on helium bubbles based on a three-dimensional lattice gas model under continued particle injection, and find that the phenomenon that pre-irradiation of helium atoms at low temperature can suppress the helium bubble growth occurs in simulation results as it does in the experiments. The reason is that small helium bubbles with high number density are produced by pre-irradiation at low temperature, and the high number density of bubbles controls the increase of sizes of helium bubbles.