first off, is the amp stable at 4, 2, 1, 1/2 ohm or what. If it is stable at 4 ohms and you are using a 4 ohm sub, you shouldn't be having this problem. now if the amp is stable at 4 ohms and you have a 2 ohm sub, then the amp is running way too hard and overheating cause you are running it at an unstable ohm rating.
If the amp is two ohm rated and you have a 4 ohm sub, all is fine in the world and it isn't overheating, but you could be underpowering it with your power wire.
If the amp is 2 ohm stable and the sub 2 ohm , all is fine.
When you state you have an impedance adapter, it sounds like you might be trying to run the amp at too low an impedance. if that is the case, you are in for some trouble. running an amp that too low impedance means that you can overheat the amp, blow the fuses, and worse case scenario, the amp blows.
My amp is 1 ohm stable, I have one sub that has dual 2ohm voicecoils, it is bridged mono to yeild a one ohm load and the amp and sub are in perfect harmony. If I put 1/2 ohm to the amp, it would be bye bye to a 1000 dollar amp. Be very careful with the impedance adapter. You more than likely don't need it to begin with. Just my .02 worth