I plan to run my aeration system more extensively anytime I get a large amount of water inflow. I have excessive water shed and believe (without experience) that turning the water over to help mix the inflow with the existing water will minimize the shock value of the sudden changes. Of course, this could be dangerous if the aeration system has been turned off for the winter and at that point I would have to play it by ear.
There's a lot of factors at play here and I would be looking at the water column temps, rain water temps, and air temps. Things like pond water/rain water chemistry is outside of my current abilities.
I would think that because it is mild weather temps and assume that your fountain has been running enough to de-stratify your remaining water column that running the fountain more constantly would be a bit of insurance. I think you're biggest risk is a bringing stagnant/dead water up from a stratified pond and/or large temperature/chemistry changes.
The above is a lot of opinion, but I'm hearing your thoughts and will watch your thread for others responses.
I can't imagine if my pond were to be only half full...I bet you've been down about it all summer!
