I don't think that the heat did the shaft any favors, but it's not like he put heat directly on the shaft... For the shaft to have been effected, he'd have had to have heated both the wheel and the brake drum so hot that the heat saturated all the way to the shaft. For the shaft to become more brittle, now you'd have to not only gotten the wheel and brake drum hot enough to get to red hot heat, but his driveway "quench" would have had to have rapidly cooled the shaft ...that's inside the axle ...that was heated red hot through thermal transmittance from a brake drum (which is basically a big heat sink) ...which was heated red hot through thermal transmittance from a wheel.
I just don't see that happening.
If it were me, I'd consider changing the shaft due to what's been done to the end of the shaft by the PO, but I wouldn't be worried that the shaft was now more brittle.
“The test of the machine is the satisfaction it gives you. There isn't any other test. If the machine produces tranquility it's right. If it disturbs you it's wrong until either the machine or your mind is changed.” ― Robert M. Pirsig, Zen And The Art Of Motorcycle Maintenance: An Inquiry Into Values