Rudy Giuliani's Hair Dye Running Down Face at Sweaty News Conference

Rudy Giuliani's sweat-fest is stealing the spotlight from President Trump's election battle ... because he appears to have hair dye streaming down his face.

The man in charge of President Trump's legal fight to overturn the election results was sweating profusely throughout a news conference ... often taking breaks to wipe his face and visible beads of sweat on his forehead.

At one point, it got so bad ... streams of what looks like dark hair dye ran down both sides of his face.

As for what's actually being said at the news conference ... Giuliani's continuing to make baseless claims of rampant voter fraud and discrepancies in multiple states, with added ire for Michigan, Georgia and Pennsylvania.