The equilibrium temperature of a grey-body is actually independent of its emissivity. A black-blackbody absorbs more radiation than a white-blackbody, but it al

The equilibrium temperature of a grey-body is actually independent of its emissivity. A black-blackbody absorbs more radiation than a white-blackbody, but it also emits more. The emissivity factors in both on the absorption and emission side, so the equilibrium temperature is independent of it. If this seems to fly in the face of all common experience, it's because things that look white aren't actually white in the infrared. Their emissivity is lower in the optical spectrum (where they absorb sunlight) than in the infrared (where they emit), so they are cooler than things that look black to us. In short, they aren't grey-bodies. The situation is also more complicated because, as you say, that things we are used to also cool by other mechanisms.