Hesitation problems gone in cold weather?

2012 Honda Civic LX, 180k miles.

First, can a transmission mount affect acceleration performance? I've been having hesitation issues (lack of acceleration power) in my Civic. The problem goes away almost completely in cold weather (anything below 35 degrees F). However in warm weather, my car struggles to accelerate quickly and it sounds kind of like it's growling.

I do believe I have a bad transmission mount due to a vibrating/rough idle that goes away whenever I shift to N or R. So I will get that replaced, but I'm not sure this can cause hesitation?

Does this sound like a dirty TB?

Fuel trims are normal. Thanks

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