OK. The motor had / has a coolant leak so the transmission's cooling hoses were replaced.
For future reference the transmission fluid is circulated to the lower radiator tank (the cool one) to be cooled and returned to the transmission.
What about the engine's coolant leak? No mention of it being fixed.
Anyway, IMHO the first thing YOU should do is check the transmission fluid. That's done after some driving, say 5 + miles, engine idling transmission in Park and the car parked on a level site. The correct level is BETWEEN the two notches on the transmission dip stick. Over fill is as bad as under fill, should be BETWEEN.
That said, you should know that when the motor is cold the transmission's first shifts are deliberately delayed to keep the motor at high rpm; that's done to quickly heat up the exhaust catalysts. So don't confuse this design feature with transmission slippage.
At 111K miles this transmission should be as smooth as a silk stocking. If you are in doubt, have the fluid changed, including draining the torque converter and changing the filter. Then leave it alone.