Hydroplaning is like sliding on ice, harder to get grip back than retain it.
Some water depth starts the issue.
Tread depth only matters on water, not on dry pavement.
And soft rubber matters.
Tire loading matters, just like on dry surfaces.
Rough pavement can break the adhesion.
Cornering, braking, steering, all use up a limited amount of friction.
They call it the friction circle, but it just means there is only so much grip you can use.http://nyracer.com/friction.htm
i recommend high performance tires for emergencies.
I've had tires that I could lock up in the rain and they would slide and still grip.
Detail- A good dry weather high performance tire will out perform an "all weather' tire in the wet.
There is a dizzying array of choices these days though.
Asd, I'm still concerned about your brake issue.
Overheating makes no sense to me.
Was it a water issue?
I would sure like to understand it.