and after all is said and done, have you checked the impedance of the speakers?
match the speaker output ohms to the speaker ohms .
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You may have the gains too high, once the amp starts clipping (overloading the input until the output attempts to drive but it exceeds the amplifier headroom and cuts the tops from the sine wave making them square on top, which essentially is like putting DC to your speakers).
Could be an issue of ventilation, should be in an area where there is good airflow and nothing on top of the amp. Also it is good to mount the amp vertical with the heatsinks running upwards to create a chimney effect.
Power/speaker wires too small can cause issues like this. Depending on current you should be running a minumum of 8 gauge wire (I believe in overbuilding this area so I run 2 gauge). Basically, when you start pulling large amounts of current through small wires they start to heat up and create impedance thereby lowering the overall amplifier output (voltage drops occur across the wires instead of the device, so instead of 12V or more you end up with less than 12V)
You could have the speakers improperly connected. If your amp is only capable of a 4ohm load then that is all you can put on it. If you parallel another speaker you will create a 2ohm load which essentially doubles the load to the amp. Some amps (older Soundstream) were 1/4 ohm stable but I have owned cheap amps that were not even 2ohm stable.
There is obviously something wrong if it is overheating. Check wires, make sure it is connected properly and then see if maybe it is the amp. Always remember it is just as easy to blow speakers with not enough power (distorted/clipped power) as it is with overloading. Not to mention that distorted sound is worse for your ears, so setting levels to what is proper for the equipment (not just to be loud) will make the hardware and your ears last longer. Plus its not what everyone down the block hears it is what you can hear that is important.
The first paragraph should have ended with... once the amp starts clipping you are creating DC in an area where there should be AC thereby increasing the heat.
Most likely your speaker cables are inadequate (assuming the ).ower cable is within spec and not overheating, too, The ole water hose metaphor may help: the pump (amp) is being asked to try to push more water (electrons aka sound signal) than the hose (speaker wire) can handle. So again assuming that your power cable matches the amps capability and is therefore delivering enough juice INTO the amp, the heat is MOST likely caused when the speaker wire / cable is too small and can't carry said juice to the speakers. Juice that don't get to the speakers gotta go somewhere, so it begins to heat the amp. If more accumulates than the heat sink can dissipate, the amp overheats and without protective circuitry, eventually fails, explodes or combusts.
Be sure you are not accidentally grounding something you shouldn't, or, check the gain on the amp, tune the deck to auxiliary, usb port, or CD without a CD in, turn the volume up almost all the way up, then tune the gain on the amp until you have less buzzing from the speakers you are powering with the amp.
It depends, is it stock or is is something you made? Amplifiers tend to get pretty hot and are able to withstand a fair amount of heat. My gut reaction is to get a larger heatsink.