Transmission or Brake Issue?? 32K miles on Vehicle

What is your question?

When the engine is cold and I start driving then slow down between 3rd and 2nd gear my car seems to hiccup and then slow down. It only does it until my car gets warm then seems to go away. I just want to make sure it is not harming my transmission or brakes. When I switch my car to auto-manual and hand downshift it myself it does not seem to do it. I cannot tell if it is my brakes or my transmission downshifting rough. This just started when the weather got colder.