Will a white object be cooler than a mirror when exposed to direct sunlight? Or will it be the other way around? If mirrors bounce all visible light and some of the other elements of electromagnetic spectrum, my guess is that it will be cooler than white objects–which only scatters light and not bounce them off. Do they reflect most infrared? What about UV light–which are absorbed by black objects?
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The answer to this question depends on various aspects. For instance when you say white object, do you mean perfectly white? or white with respect to only visible light? Same happens for a mirror too.
The most direct way to look into the problem would be following. Mirrors are nothing but extremely fine and optically flat white surfaces at the back of glass. Usually its silver coating. Silver when left alone as a lump can act as a white object too. Now we can reformulate the question by asking: Will a fine surface of silver absorb less heat than a lump of silver? The answer is their absorption co-efficient is same. So heat absorbed per unit mass will be same.
But mirror looks more brighter as if it reflects more light than white object. The answer to this is that usually white objects do not have flat surface. So the reflection is not regular unlike mirror.
P.S. If you consider the glass of mirror through which light has to pass, you'll find that some light is absorbed their. So reflectivity of mirror is actually less.
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$\begingroup$ There are front-surface mirrors, bandpass mirrors, dielectric mirrors, etc, so you answer is correct but a bit incomplete. $\endgroup$ Apr 19, 2016 at 15:19
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2$\begingroup$ I completely agree. That is why I emphasised on perfect mirrors and left the conclusion for normal mirrors only as post script. $\endgroup$– AriApr 19, 2016 at 19:49
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$\begingroup$ If we use this in real world situations such as car paints, considering metallic paints are the most reflective type of paint, between metallic white and metallic silver, which would absorb more heat? $\endgroup$ Apr 20, 2016 at 5:04
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1$\begingroup$ In car paints, "silver" just means "grey". I doubt they put silver in the paint! Then, grey paint absorbs more energy than white paint (by definition of "grey" and "white"), if we assume they have equal "metallicity" contents. $\endgroup$ Apr 21, 2016 at 9:56
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$\begingroup$ Glossy white paints and mirrors are lies in the world. :C $\endgroup$ Jun 1, 2016 at 22:12