"standby" and "idle" are two different things!
In "standby", all the circuits in the integrated amplifier are shout-off except drawing small current to provide power to lite up the "standby" LED and maybe some control circuit. Therefore the heatsink should be at room temperature.
At "idle", all the circuits (DAC, preamp section, power amp section, control circuits) in the integrated amp are on, only there's no source signals input. The class AB power amp section will run at its class A bias. Hence the heatsink temperature is higher than ambient temperature.