Hey, I am an aspiring musician and sonic enthusiast.
I know from experience that speakers DO need breaking in, however, breaking in of amplifiers is dependent on two factors: One, the complexity of the amp, two, the sensitivity of it's components. If it needs to be run for 36 hours before use, at least do one break in just to see if anything changes. A break in involves selecting a piece of music with a wide dynamic range. Turn the amp to at least 60% of maximum volume. Then rock out for 5-10 minutes. If you can't do this without disturbing your neighbors, you will have to do this at home. Then turn the amp off, or stop the audio and allow the system to cool down. You may then use it normally. This is not much different from the process of breaking in speakers, only speakers take a few days rather than just 5-10 minutes. This should give the amp a much better response. The piece of music I recommend and do all of my break-ins with is DJ Irek - Space Driver.

Do note: this most likely will only affect amplifiers with large electrolytic capacitors (those large can looking things) and induction coils. (The bundles of wire you see through the vents.)