Yes, it's very easy to fit a fan that will run after the engine's switched off. This will certainly help with your static overheating problem.
In the UK they're made by Kenlow and sell for about 90m quid, but I don't know if they're available across the pond.
A side advantage is that they can be set to cut-in at any temperature, so you can run the engine cooler and make things easier when you stop.
Any electric fan and temperature switch from a breakers yard can be made to do the job you need, but it will need a bit of "hands-on" inginuity to make it fit......
'73 Jensen Interceptor (Resting)
Giant Full Sus Mountain Bike