I assume the 360s is similar to my 36 which stays just as warm in standby as it does during operation.
To quote the manual for the 36:
"Pressing standby again places the No36 into standby mode, which turns the display off, turns off all outputs, and disables the front-panel controls. The internal circuitry remains powered up in order to maintain its thermal stability and optimum performance at all times."
I think this is normal for your 360s.