No.
What does happen to me is that I am always pretty cold. Everyone says I have cold hands all the time, which I don't notice, but if I sit down or lie down then yes, my temperature drops when I'm not actively doing something and then I feel cold. I must have one of those on/off metabolisms that fires up a lot when active and shuts down the minute I just stop doing anything. Or crap circulation. If you are depressed then you tend not to be feel like being active, sit around or lie in bed more and you'll probably have lower body temperature as a result. If something's bothering me then that's exactly what I do... sit around and brood. And get cold.
Your transition just started I guess and it won't be like flicking a switch and you'll instantly feel exactly as you want to be, it's going to take some time. At the moment I am hovering on that point of still wondering if T is going to have the result of results I hoped for. But I know it's going to take a while and there's nothing I can do but wait. Which is depressing but better than the stage where I didn't even know if they were going to accept me for hormones and surgery... at least you're on the road, instead of sitting on the wall wondering if you'll even be allowed on it.