I know that white reflects all of the visible spectrum, but our Sun is a yellow star, so a yellow car may get less hot when exposed ?
An object which appears to our eyes as yellow in sunlight is absorbing the blue part of the sunlight and converting it to heat. So a yellow car aborbs more light than a white car - and so heats up more than a white car.
What about the metalic grey which mimics the back of a mirror ?
We would consider an object which reflects ~30%-70% of incident light to be grey - grey means it absorbs all colours uniformly but not brightly. 'Metallic' as a paint finish just means it has optically flat particles in it. So 'metallic grey' still absorbs lots of light to be considered grey.
On the other hand, the most of the heat is maybe not absorbed in the visible, so, in that case, what kind of painture to try in order to reflect, say, infrared ?
You would need to find datasheets from specialist paint manufacturers. One of the most reflective white materials used in optics is Barium Sulphate with 98% reflectivity extending into the near IR, but it is not hardy for use as a vehicle finish.