One piece of advice is to look at how the uke reacts when it gets hot or cold.
Yes an Outdoor uke can cope with being hot and cold. No you can't play it when it is hot, you wont be able to hold it and it wont stay in tune. This is true of most ukes, even wooden ones which survive. So while a uke might be able to get hot and cool down without damage, you wont be able to do much with it when it is hot.
I suggest a Mahalo U30 (not made anymore you have to find a used one) or similar with a good set-up and strings. Hanging by your hat or coat in the hall or entry. When you go out you put on your hat or coat or both and pick up the uke and put it in the car, which wont get hot while you are in it. When you park, make sure the uke is out of direct sun light, maybe wrapped in a layer of insulation like a towel, if you are not taking the uke along. When you get home or to the workplace hang the uke up with your hat and coat. You wont need a case or a bag for this uke.
The OutDoor uke is a great outdoor uke. You are not outdoors sitting in your car. Its great strapped onto a backpack or bicycle rack on an adventure. Its not going to be much use after spending a few hours in a hot car, nor is any uke for that matter.