Hot is still relative. Are you talking about soup, a cup of coffee/tea or outside temperature? People would probably answer differently in each instance.
They were once marketed as being from Tangier, a city in Morocco where a few are grown. They've more recently been called Mandarins, because they're in fact native to China.
That nitrogen is fixed inside root nodules on the root system of the bean plants. It's taken up by them immediately. It's not available to the corn or anything else growing nearby.
That nitrogen isn't really made available unless the plant has been turned into the soil as green manure at flower. Harvesting the bean crop (protein/nitrogen rich itself) leaves the soil about neutral, maybe somewhat depleted depending on how the field is cleared and prepped for the next planting. Also, there's research showing that some corn can fix some nitrogen itself on the slimy exudates of aerial roots.
At some point I learned to clean as I cook, washing each item immediately as I'm done with the step that uses it. If you can get in the habit, it's so much easier. Never a huge stack to clean and nothing sits there getting stuck on the pot/plate/whatever. Dishes are done before sitting down to eat and there's only a couple when you're done eating.