Running hot shouldn't really give you the problems you are experiencing, however, amps do tend to run pretty hot. However, the cooler you can keep it the better. By keeping it cool you can prolong its life. For tons of really helpful, easy to understand info go to:
http://go.to/bcae
It should have info on how to mount fans if you want to.
So we have these facts down:
1. If you switched speakers, and the problem switched too, then the speakers are good, the problem is upstream. If the speaker itself was bad, if you switched the wires, the back rear would have played like normal (good). So if both play bad, then it's upstream.
2. Next, you checked the amp. Now here is the thing - if you change the RCA inputs, did the channel that was messed up on the amp stay messed up, or did a new channel get messed up? I'm a little confused on the word "driver" you are referring to, but it seems to be that when you're changing the RCAs, the channel that is messed up on the amp changes too. If that's true, then it isn't the amp, it's still upstream. If you switched the RCAs, but the same channel was still cutting in and out, then you'd know it was the amp.
So the last thing it could be would be the head unit or the wiring in between. I suspect grounding problems. Make sure that your wires are all connected securely behind the head unit and that the RCA connection parts are not touching other metal parts as with the rest of the wiring, like ensuring the solder, heat shrink, or electrical tape is still working. The common prob with Explorers is that it gets REALLY hot behind the radio, so sometimes the electrical tape just goes to slag. Also, follow the RCA path, just to make sure it's not rubbing against any bare metal and hasn't accidentally been cut into by foreign objects. Same for your amp power wire that might have gotten caught in the firewall or something.
Try and fix the prob within the next two weeks if you have time. Constant grounding will hurt the components if exposed for a long time.
Jon