Not just this happens to me. But I can totally relate in the way I feel like you stutter more when "your engine" is cold. That's why I am starting a routine of every single day when I wake up I go straight to my phone and start recording and start talking for 10 minutes about anything that is on my mind. Besides helping me in talking, it also helps me a lot to project what's ahead in the day and put my ideas in order. I am noticing some difference and I just started a few days ago. Still a long way to go tho. The only thing I can think of to avoid a big stutter is like don't try to rush what you are going to say and just speak slowly. I feel like feeling calm plays a big part on this as well.