Always power off when making connections like this. Then it will be okay to leave on with nothing connected.
The amp btw was fine. For every watt of power you get about a watt of heat. Touch a 300 watt light bulb for reference. That's how much heat the amp has to dissipate, one way or another. If you run one 300 watt amp so hard it gets hot then guess what? Next one will too. Maybe not where you put your hand, but that same heat does have to go somewhere.
The amp btw was fine. For every watt of power you get about a watt of heat. Touch a 300 watt light bulb for reference. That's how much heat the amp has to dissipate, one way or another. If you run one 300 watt amp so hard it gets hot then guess what? Next one will too. Maybe not where you put your hand, but that same heat does have to go somewhere.