If you have a noncontact voltage tester you simply need to touch its tip to the wire youre testing. A warm switch can also be caused by loose wire connections so check these.
Furnace Disconnect Requirements
Disconnecting a light switch. If you have to leave the circuit energised then you cannot plaster over the light switch and will have to fit a blanking plate. Gently pull the entire light switch assembly outward away from the wall so that the wire terminals on both sides of the switch are exposed and able to be easily worked with using a screwdriver. The light will go. It can be as easy as removing the switch and wire nutting the two wires together attached to the switch. You only need simple tools and materials to do this. To disable a light switch remove the two wires from the switch and tie them together with a wire nut.
With the power off of course. Now if you find that when one wire is connected at the bottom it controls only the plug and when the other wire is the only one connected it controls only the light if you get a different effect post back with the exact details then. Then putting a solid cover over the box. Now disconnect the other bottom wire and reconenct the previous wire to the bottom now check the switch it should control the oposite item mark it. Find out what circuit it is on and isolate that circuit disconnecting the cable to the fitting if possible. If the fixture is controlled by a pull chain trace the wires from the fixture to the point where they connect to power.
Is the overhead light on a different switch or do. You need a slotted screwdriver two wire nuts a blank light switch insertor blank wall plate and possibly some electrical tape. Loosen the terminal screws until the bare wire ends move freely. A switch rated for 15 amps installed on a 20 amp circuit may heat up if its controlling a number of light fixtures or devices that draw more than 15 amps of power. If so then you should replace the switch with a properly rated 20 amp switch.