Here is an idea, not sure how long it would work but it is just an idea.
Get an ice chest like a 48qt. or larger. Plumb an inlet and outlet into it and get a small gpm delevan or shurflo or flojet pump.
Get some copper tubing to wrap around the motor and put fittings there at the motor so this can be disconnected easily without having an ordeal to work on the system.
Plumb some hose from the ice chest to the pump to the coil and back. Fill the ice chest 1/4 with water and the rest with ice, maybe some rock salt to help keep the ice cold. Run the pump when it starts getting hotter in the day.
Maybe the cold water circulating around the motor will help keep it cooler but there will be condensation there at the motor which might lead to other issues like possible rust, algae or mold.
Not sure how long the ice will last but as long as the water is cool, it might help.
I don't think it would cost too much to give this a try.
You would probably have to empty some water and add ice a couple times a day or more.
With the pump running, it would have to be connected to a good battery or rig it up to your remote so you can turn it off when working.
If you had a small refrigeration unit to help keep the water cold, you could have cold water all the time but that is more work and more cost involved.
Just an idea.