I want to point out that freezing the gear is the opposite of normal practice. Most gears.are heated for expansion to do the same job, some even freeze the crank. Either method seems to work. I don't know know metallurgy for brass that deeply, I was told (not read) it was the brass's contraction properties, thickness, diameter, and hole diameter in combination that made it work. A cold gear is easier to handle than a hot one, I had no issues, got paid by the hour and did as I was asked. I did my own that way 3 times after. Did I get lucky? I didn't do the math.
That said, the main advantage would be the bearings might not need pressing to the frame because that is the outer diameter of the bearing and the OD is shrinking for sure. My not fully understanding about the motors gear was an ID contraction based thing. If the gear contracts, seems the hole should too????? Math is needed before I'll ever truly understand what I was doing.