My understanding is that, everything else being equal, there are three primary factors that determine how hot a surface feels in the sun:
1) Solar Reflectance: the fraction of incident solar energy which is reflected by the surface
2) Thermal Emittance: the ability of a hot material to shed its heat in the form of infrared radiation
3) Thermal Conductivity: the ability of a material to transfer heat through direct contact
Polished chrome and polished aluminum have high reflectance, but also have very low emittance and high thermal conductivity. So, even though they do not absorb as much energy from the sun per second compared to other materials, they cannot shed the heat energy and eventually become very hot. Furthermore, their high thermal conductivity causes the heat to transfer quickly to your hand.
Painting or adding a coat of plastic will reduce the thermal conductivity so that door handles at the same temperature will feel less hot to the touch. And adding a coat of paint to the polished metal will typically reduce the reflectance but will also significantly increase the emittance so, depending on the scenario, the overall temperature may actually be reduced (c.f., white painted metal roofs are often significantly cooler than bare metal roofs).