It has been shown that a single-domain magnetic nanoparticle can be effectively switched by a linear down-chirp microwave field pulse (DCMWP) in zero temperature limit. However, finite temperature is ubiquitous in practice. Here, we study the effect of finite temperature on the DCMWP-induced magnetization reversal based on the stochastic Landau-Lifshitz-Gilbert equation. It is found that any one of the three controlling parameters of a DCMWP, i.e. the amplitude, chirp rate, or initial frequency, decreases with increasing temperature while the other two are fixed. The maximal temperature at which the reversal can happen increases with enlarging the system size. These phenomena are related to the facts that the energy barrier induced by anisotropy increases with the system volume, and the effective magnetization decreases with temperature. We also provide a set of optimal parameters for practical realization of our proposal. These findings may provide a way to realize low-cost and fast magnetization reversal with a wide operating temperature.