GM electronic auto transmissions do a sort of wear sensing thing that modulates the fluid pressure to adjust the shift harshness. As the internal clutches wear, they increase the line pressure to hold the clutches. The transmission fluid changes viscosity with temperature, and it could be that your transmission fluid is getting old and roasted, or your filter is getting clogged. Then, when it gets hot, it shifts too hard. You can reset the shift program by resetting the ECU so it relearns the pressures, but I'd change the fluid and filter first. I really like Dexron VI synthetic, even in Dexron III transmissions. It is much more stable over temperature. You need to make sure to flush all of the old stuff out, though. It should take about 9-12 quarts of fluid.
I would also check/change the engine and transmission mounts as they are bound to be old and cracked. This will make a difference to shift feel and general clunks by absorbing the driveline slack better.
Edit: Wait, did you say new transmission? If so, you definitely need to reset the ECU so it will reset the line pressure to factory default.