The hum from the front of the amp IS from the power xfrmr. It's probably a result of DC on your incoming power. It is almost certainly not a ground loop. As far as how hot the amp runs normally, that depends on a lot of things, including how far into CLASS A the amp is biased. Also, while the nominal spec on the 683 is 8 ohms, there are some reports on the web that they dip to 3 ohms within the audioband. The Adcom's published power specs show that while the amp is rated for a 4 ohm load, the power output does not "double down" and the rating is for continuous average power, not RMS. both of these factors lead me to believe that the amp is not fully capable of driving low impedance loads and that may be why the amp is heating up. Or it could be normal, or it could be that it needs repair. Maybe some of our more tech savy members can say if the DC leakage could cause it to run hot.
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That seems like its running a little warm to me. The noise coming from the amp probably is the power supply; I can hear a slight noise coming from the power supply in my dac, snd two external power supplies that I have also. The hiss is normal too in my oppinion; be thankful it's not a hum (ground loop hum) because if the hiss is slightly bothering you, a ground loop hum would drive you nuts. Removing your ground pin might lead to shocking results ;-)
Definitely not a ground loop hum, as that would be from the speakers. Here's a good read about transformer hum,
Also, here is an owners manual for the 5503,
The troubleshooting section has a little about amplifier hum. The manual also states that the amplifier is OK to use with 4 ohm speakers, and is stable to 2 ohms and less, so the 683's should not be a problem.
Swampwalker, sorry to disagree, but continuous power is RMS power. Adcom inserts the word "average" because in the manual they make a reference to the FTC, and a lot of times in the FTC documents, the terminology "continuous average power" was used to explain the standard. Most of the time it is just stated as "continuous power".
This series of Adcom amps do have a history of running hot, but what is too hot may be hard to determine without putting it on a test bench. Maybe Adcom tech support could help with these issues.