i wasn't aware of any power plug issues with the modi, and as for heat, i've had the modi 1, and i currently have a modi 2 uber, it stays on all the time, and it's as cool as the underside of a pillow
now, the magni gets a little warm i know, could you mean the magni ?
i recall someone on this thread has a magni/modi combo, said it was overheating. I wondered at the time, how can a DAC overheat? So, yes, probably the Magni was the culprit.