Measured across... the resistor? Circuit on or off? Units? (ohms, volts? I don't even know what you're measuring)
A whole bunch of people have looked at the tangentsoft site, and there's nothing untowards about that circuit. Just out of curiosity, what's this new schematic and what's better about it?
10 seconds while playing music (how loud, into what headphones) or not? Estimate of temperature? Which op amp, the 741 again? Regardless, that seems pretty much like it can't be right, even disregarding the one channel not working. Pretty much no op amp should be getting that hot that quickly with +/- 9 Volt rails.
Either the circuit's not wired right or the op amp is fried (from say being miswired before) and shorting internally. If there's a short inside, that would explain the rapid heating and also a channel not working, but it also could be that the circuit's wrong.