If nothing was plugged into the circuit and it tripped the breaker, you've got a short somewhere...maybe not a constant one, or it would trip as soon as you turned the breaker on. If there is a loose neutral wire somewhere or the neutral touches the ground wire, you could get it to trip. You're right, it isn't a good idea to feed one gfci from the load side of an upstream one.
Do you know what else may be on that circuit? If you turn the breaker off, is there anything else that doesn't work? DW, frig, something in another room? Lights?
The wires normally wouldn't get hot unless there is current running through the wires, so if nothing is plugged in, there should be no heat. I suppose it is possible if things are really tight, the room temperature rising through the day could cause things to expand enough to maybe short against something.
While this is by no means a definitive test, if the gfci works and you trip it with the test button, you've got a fair but not 100% guarantee is works right.