While the reg might be dying of heat exhaustion with nothing attached to the output, it should be pretty reasonable with a load attached.
Unloaded, going from 38v to 24v is asking a lot of the regulator. Still in spec, but you start to need a pretty serious heatsink whaen you get anywhere near 10v, even. A 24v 400mA wart with regulator and amp drawing 105-135mA should swing that voltage way down. I'd take a WAG and say to maybe 28-29 volts? Possibly lower. Unloaded, the regulator will not be happy without a large heatsink.
What is the voltage at the input to the regulator with the load attached and running?
...oh I see... it looks like 27.7. You should be fine, even with a modest sink and ordinary silicone grease. That's about as low a differential as you would want to go anyway. Meaning that if your amp was to draw more current, the differential gap would narrow, and you will likely fall out of regulation at times, depending on the line voltage to the wart.