It would help but the glass windows (greenhouse effect) are probably a bigger factor.

Good window tints (with IR and UV blockers) help big time keeping the car cool.

We need integrated pop up solar car awnings that provide energy and shade. They actually make funky pop up car awnings, but a sleeker, solar option would probably take hold in hotter climates.

How does that compare the the fraction reflected by a white paint scheme?

You can have your cake, eat it and get icing on top by using a coating that

a) has a transmission window in the range that's useful for PV b) has high emissivity in the atmosphere's IR window c) has high reflectivity in the rest of the spectrum

That’s awesome. Either we don’t have those materials nailed yet, or the demo version pictured has the cells showing for presentation purposes, or both.

Edit: third possibility described by the interesting reply below: there could be an out of visible band reflective coating over the panels.

Cells with such a coating would still appear dark to the human eye because the visible spectrum contains the peak of sunlight's energy distribution and you want to convert that to energy (you could optimize around the UV/violet range since the excess photon energy gets converted to heat there). But there's a broad limb of IR in the distribution that is useless because it's below the bandgap of most PV materials, that's the part you want to reflect. But then again inside the IR range there's the IR window, where you don't want to be reflective to increase emissivity to shed heat into space.

I have read research papers about such coatings, but I don't know whether they're in commercial use.