Influences of temperature of medium on proton conductivity in hydrogen-bonded systems exposed in an electric-field are numerically studied by the fourth-order Runge-Kutta method with our model. The results obtained show that the proton soliton is very robust against thermal perturbation and damping of medium, and is thermally stable in the temperature range T ≤273 K. From the simulation we find out that the mobility (or velocity) of proton conduction in ice crystal is a nonmonotonic function of temperature in the temperature range 170-273 K: i.e., it increases initially, reaches a maximum at about 191 K, subsequently decreases to a minimum at about 211 K, and then increases again. This changed rule of mobility is qualitatively consistent with its experimental data in ice in the same temperature range. This result provides an evidence for existence of solitons in the hydrogen-bonded systems.