An Analytical Band Monte Carlo model was used to investigate the temperature dependence of impact ionization in InAs. The model produced an excellent agreement with experimental data for both avalanche gain and excess noise factors at all temperatures modeled. The gain exhibits a positive temperature dependence whilst the excess noise shows a very weak negative dependence. These dependencies were investigated by tracking the location of electrons initiating the ionization events, the distribution of ionization energy and the effect of threshold energy. We concluded that at low electric fields, the positive temperature dependence of avalanche gain can be explained by the negative temperature dependence of the ionization threshold energy. At low temperature most electrons initiating ionization events occupy L valleys due to the increased ionization threshold. As the scattering rates in L valleys are higher than those in Γ valley, a broader distribution of ionization energy was produced leading to a higher fluctuation in the ionization chain and hence the marginally higher excess noise at low temperature.