1993 Mazda MX6 Electrical issue

Gotta see it to diagnose it. What doesn't work? There's wires carrying high current for the head light dimmer switch, turn signals, wipers, and ignition switch. Any of those can have a connector terminal that develops a little electrical resistance which translates into heat, melted connector bodies, and more resistance and more heat. These types of things act up after the circuit or system has been turned on for a while.

To get hot so quickly after starting the engine suggests a wire that is grounded out or two wires shorted together. This is more common on cars with tilt steering columns that get moved a lot.

If the car has an air bag, there's also a "clock spring" under the steering wheel that could be coming apart. That's a wound-up ribbon cable with circuits in it for the "initiator" for the air bag, and any other switches on the steering wheel. Those usually carry very low current so they're unlikely to get hot.

Slow down. No need to waste time and money. A code reader isn't going to help with this. On '95 and older models all that's monitored is engine-related stuff. You need a full scanner to look for diagnostic fault codes in Air Bag, Anti-lock Brake, and Body Computers. If a power wire feeding a computer is shorted, it will blow that fuse, then that computer won't even turn on or communicate with a scanner. All the other wires don't carry enough current to cause smoke.

If you have an aftermarket radio, check if someone spliced a bunch of wires behind it and wrapped them with electrical tape. Tape should never be used in a car because it will unravel into a gooey mess on a hot day.

Don't just randomly replace all the fuses. Just check those that are for the radio or anything else that's not working now. If the fuses aren't labeled, they have two small holes on top to stick a test light probe to quickly test them without having to remove them. There will be two radio fuses. One is for the switched power from the ignition switch and one is for the station preset and clock memory. That one is always tied in with some other system that's always live like the interior lights, cigarette lighter, or horn.