Spectral type isn't 1-1 correlate with the star estimated life. Depends on the star mass. Our Sun was one time a F type star.
By estimating how much starlifting would explain the observed luminosity drop, and then backing out the expected increase in the star's life against its flux decrease one could estimate how efficient the "aliens'" energy-harvesting technology is (coupled to a financial discount rate).
[1] https://en.wikipedia.org/wiki/KIC_8462852
[2] http://astronomy.swin.edu.au/cosmos/M/Main+Sequence+Lifetime
http://www.popularmechanics.com/space/deep-space/a10885/the-...
Of course if this was happening we'd see some unusual proper motion from KIC 8462852. Which we're not. (Did someone check?)
Of course there would be all sorts of secondary effects, lowering the density in the core could slow down the rate of fusion, increased temp would increase it, but no garuntee that the effects would cancel. Also depending on how far out your mirror is the core might not ever notice the change. The outer layers could heat up and destroy your mirror before the increased temperature reaches the core.