How warm can power cables get while still being Ok?
Most circuit breakers, wire, and equipment are designed to operate up to 75°C which is 167°F.

Normally, they are not that hot, but if they are fully loaded they could become hot enough that you don't want to hold on to them for very long.

Body temperature is pretty cool for a cable operating with a reasonable load on it.

I would not worry until it burns your hand to touch it.