This is somewhat easy to do if you have a roof-rack or somewhere similar on your vehicle to mount a small-ish panel, and you are handy and understand your vehicle's electrical system (though this may be tough with newer models since everything isn't controlled by simple switches any longer).
Basically, mount your panel, and install a block diode if it doesn't already have one, then run the wires (positive and negative) to your battery to keep it charged.
Then, all you need to do is hook up a switch to your blower motor inside the vehicle, along with a simple speed controller (for this, it's best to use a cheap 12 vdc PWM controller - don't try to use the "low speed" resistor if your car uses a resistor pack, as it might not keep it cool enough) - so you can turn it off and on, and control the speed of the fan - while the car is parked and "off" (no-key).
Park it in the sun (of course), set the vent controls to allow air in from the outside (hopefully it stays this way when the car shuts down - if not, you'll have to figure out a way around that), crack your windows slightly (1/4-1/2 inch), then shut off the car. Flip the switch and set the speed control for the fan to something "low" - the fan should run, but not at hurricane speed.
Then get out and close/lock the doors. Air will be drawn in from the cooler outside, blown into the cabin, and exhausted out the windows.
The battery will stay charged from the solar panel.
If you are concerned about the battery being run down when the sun sets, then:
1. You can optionally use a separate battery to the fan, with a blocking diode to keep the fan from using energy from the car's battery.
2. Or you can add a thermostat to detect and only run when the sun is beating down hot (this could be in addition to the PWM control - so the fan doesn't run all the time, only when the cabin gets too hot).
3. Add a photoelectric switch to disconnect the fan from the battery, when the sun goes down.
4. A simple way would be by just wiring a standard Bosch SPST automotive relay (the coil) in series with the panel, and the fan across the contacts - when the sun goes down, the relay would open up, and shut off the fan.
Note that this car ventilation mod does not require an Arduino, so you might not become popular or upvoted on the tubes, but your car might be cooler in the summer...