Interesting thread. From my own experience in heat treating various bullets for long range handgun your all more or less right.
Different weight bullets cool at different rates and does affect the final BHN. This is the reason ingots should not be tested with a bullet BHN tester. A 1 pound ingot will cool much slower and the final BHN will be much softer than a 200 gr bullet cast from the same ingot.
Different BHN bullets with the same load (bullet, charge, crimp, primer etc) does change the group size, velocity and standard deviation. For examples: My FA 357, RCBS 180 gr silhouette, 14.6 gr H-108, CCI 550 primer, all tests with virgin WW brass.
22 BHN bullets
Extreme Spread - 25
Average Velocity - 1455
Standard Dev. - 8
18 BHN Bullets
Extreme Spread - 18
Average Velocity - 1495
Standard Dev. - 6
Both tests fired on the same day and all components from the same lot numbers.
Other cartridges show even more variation with no change other than Bullet BHN. In this FA 18 BHN gives both the highest velocity and the best groups. The further from 18 BHN in either direction the worse the groups and the slower the velocity.
BHN's within a range shows no variatoin on the chronograph. Example 14-15 BHN. 17-18 BHN. 21-22 BHN.
So to answer the original question in this thread. Yes, air temp probably does affect the final BHN BUT, my air cooled WW alloy is 11 BHN, if I cast outside on a cold day and they turned out 12 BHN there would be very little to no difference in how they shoot.
My 2 cents worth from my experimenting. Hope this helps.
Rick