PC Engine RGB amp and THS7374 heat problem

I have installed some of the PC Engine RGB amp PCBs designed by Mickcris using the THS7374 chip and by chance during testing noticed that the chip became extremely hot. Obviously it shouldn't be that way and so I tested the chip on the PCB I had installed in another console and that too was way too hot.
The first thing I concluded was that I must have done something wrong, but I tested further with some other of the PCBs and the result was the same.
I have also used some of the THS7374 on some of the SNES RGB PCBs designed by Borti so I tested my SNES and SFC to see if the chips on these were hot, which they were not.
The difference between the PC Engine and SNES PCBs is the SNES using the fourth channel for sync (both boards have low pass filter off), and as the PC Engine doesn't use the fourth channel, the board has the input and output connected to ground. I lifted both the input and output legs of channel four from the PCB and then tested again and the THS7374 chip didn't become hot.
So for someone more knowledgeable than myself, is it good/bad/necessary to connect unused channels to ground or leave them floating? It seems in this case a bad idea to connect them.

 

Output shouldn't be connected to ground.

 

Input can stay grounded, output should be floating. If the chip is still working, that is ;p

 

How come nobody else noticed this? The board was designed by Helder and Mickcris and is widely available.
There are probably a lot of PC Engine consoles with hot THS7374 chips.

 

It's hard to believe someone designed an amplifier board to power a short cut.
There must be some mistake somewhere.

 

Yes, it must have been a mistake, but there are probably a lot of PC Engine consoles out there with this RGB amp PCB inside them.
I have lifted and broken off all of the fourth channel output legs on the amps that I have.