The photosphere could get quite a bit hotter than you might think if you reflect 50% of the energy; after all, almost exactly 100% of the energy emitted by the star is currently lost. Heating the outer layers increases the temperature, there fore the luminosity- you then reflect 50% of the increased luminosity back to the star.
By reflecting that energy back to the star you are heating the star up from the surface inwards. The photosphere will get hotter, therefore more luminous, well before the increase in temperature reaches the core.
Since the star expands when it is heated in this way, that would affect the density- I wonder how that would affect the rate of reaction at the core?
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