When I first start my car the last few days (A 2008 Toyota Camry that I've had since it was new in 2007, 13 years) the temperature needle ends up slowly climbing past the halfway point all the way to the top. Only then, about two minutes into using it, does it slowly drop. It takes about a minute more until it stabilizes at the midpoint and stays there until I'm done driving my car
This happens, generally, after each time I leave it sitting for more than a few hours. Sometimes it doesn't climb all the way; sometimes it just goes a little above the middle before dropping and stabilizing
The first time I noticed it, I heard what sounded like an extra set of fans kick on when it got all the way up, which quickly cooled it down to the middle
Running the AC might be making it worse – making it go up faster? But it seems to go up regardless of whether the AC is on or not. My AC was recharged (for the first time, I believe) about two months ago...