But weather-wise, September is a good time for clearer skies. One of the best times of the year besides October IMO.
25 minutes is tight there, depending on the time of the day. Remember, you need to exit security to connect, and re-enter with all of the other passengers. If there is a DEN, LAX, and SFO flight all leaving at the same time, you could get left behind. But the staff there is great, and they know the customers are there because they like the small-airport feel.
I have heard on FT, that if you identify yourself as a connecting passenger, at the gate that lets you out into the non-secured area, they may let you into the gate area with the other folks waiting for departures.
Good luck!