Yeah.....Power (dissipation) is what causes heat!
Running the amps idle isn't causing it to over-heat! Now, if it is a Pure Class A topology, those tend to run hotter at idle than a class A/B or class D amp. If you want to learn about this, go read up on amp topologies, biasing, and quiescent current.
The general rule of thumb is to place your hand on it. If you MUST pull your hand away due to the heat, then it's too hot. If you can leave your hand on it indefinitely, then it's fine.
Now, you may have some issues going on causing excessive heat, but running (properly functioning) amps at idle won't do it.