Try replacing the switch, making sure to use the screws to attach the
wires firmly to the new switch. Don't use the back stab wire inserts.
Also, if the wire insulation has become brittle, make sure to wrap it
well with good electrical tape, or if you have enough slack in the
wire, cut the wires back to where the insulation is pliable.
Also, before turning the power back on, check the wires in the
junction box that the light is attached to. Make sure they are in good
shape and attached firmly. If the insulation is brittle, cut back to
where it's pliable if slack permits, or wrap well with good electrical
tape.
Watch carefully. If the switch gets warm again, something else is
wrong, and you'll need to get it diagnosed.
Also follow Colbyt's advice for the 3-way switch scenario.