66 Dart 270 Brake light fuse heats up??

The problem could be as simple as bad connections right at the fuse, IE bad fuse, bad fuse clips, poor connection between the fuse clips and the terminals in the back of the fuse box, and of course bad / corroded/ loose connections right at the wires

In addition to other posts above, you need to find out what is REALLY (actually) supplied from that fuse. Measure the current draw with a multimeter. This is easy to do. Get an inline fuse, same rating as whats in the box and remove the fuse from the box. get some good alligator clips and clip onto the fuse holder

Wire it From fuse clip.............to temporary inline fuse.........to multimeter........through the meter...........to remaining fuse clip

Carefully set your meter up for amperage and see what it draws.

Your factory service manual has a chart somewhere near the wiring diagram section showing what loads are on that fuse.

THIS.

Replace the fuse? If so, NO CHINA. There have been recalls and fires.

Try tightening the clips or look at the clip that holds the fuse. ANY signs of arcing?

Try measuring the voltage drop along the circuit. Voltage drop is FAR more effective for determining wire condition than ohm tests. But the heat will be where the problem be.

The side that's physically hot is either the source side or the circuit side. Which was it?