Odd problem, but based on the randomly running hot comment, I would be checking the cooling components and their power supply. Does the radiator cooling fan spin freely by hand? If not, replace it cuz bearings are bad. If it does, you still need to look at the battery (load test it), and cooling fan relay and wiring harness to it. Might want to just replace the relay to eliminate it as a possible problem down the road.
Don't know exactly why it would affect the radio but under high amp draw the electrical system will do weird things especially if you have bad or missing grounds. Low voltages will sometimes keep other relays from "connecting" keeping whatever they control, OFF.
Could be as simple as a weak battery. Could be a bad CF relay, or fan. Could even be a combination of a few things working against you.

 

Keep in mind, there are 2 fans. One is A/C (condenser)fan, and the other is the main cooling fan. A/c fan runs when A/C is ON. Cooling fan only runs when therostat control says to. That thermostat could also be your culprit. Look on kiatechinfo.com for more details.

 

Just a thought check your X01 connector for your fuse box for burned or loose connectors
or whatnot. Use http://www.kiatechinfo.com/ if you live in the USA for help that is the only thing i can find in common for your electrical issues from my book Reguard's Ronjohn