Since you say you have an oscilloscope I will assume you have a multi-meter. To rule out if it is a ground / power wire problem, measure the DC voltage directly at the amplifiers power terminals (directly where the 12v+ power & ground wires go into the amp) while driving it as hard as you normally would (or the volume where it is getting hot), and see if it drops real bad. If you have a bad ground / power wire connection the voltage will drop under load from the added resistance from a weak point in the circuit path. If the voltage stays the same or is within operating specs of your amp then I would have to say the problem is somewhere else.
I do not know what subs your running or the voice coil specs, but if it were wired too low it could be the cause of your overheating; accidents happen when wiring sometimes. I am sure you have it wired right, but never hurts to double check if you did any wiring to them before changing to the Soundstream amp.
Amps do get hot by nature when running them towards the upper end of there power range, but as long as it is not burning your hand & you can keep your hand on it, it may be operating normal. Now if the amp is actually shutting down in protect mode, then you definitely have a problem & possibly with the amp. But check all wiring first.