Alexandrite cannot be improved by any kind of thermal treatment. Although some have tried, heat treatment does not seem to affect alexandrite at all. Some lower quality cracked alexandrites are oiled to hide the cracks but beyond that, alexandrite is not known to be treated in any way.
Some customers prefer cat's eyes with brownish hues and chrysoberyl cat's eyes can be irradiated to produce this color. This kind of treatment is not common and is easy to detect by any of the well known labs that are set up for that.