[strictlypersonl]

Unless you've been bleeding the brakes, fluid from the reservoir never gets to the master cylinders. The hot fluid in the lines stays put. If their fluid's color is turning brown, it's from leaching from the hose, not overheating.

A slight addendum...
The fluid in the hose does work its way down to the master cylinder as the brake pads wear and the piston's rest position moves out. That, however, happens very slowly, over thousands of miles.