Hello. You do not know what time the box will arrive, just which day, and you pick which day you want it. I have never had anything spoiled or overheated in our box; there are "ice packets" in it.
So as far as choice of meals... when you first sign up you can make choices about things you don't want. We selected no seafood and no walnuts. I wouldn't go crazy opting out of stuff; you can imagine that takes away so many options for delicious recipes. If you have a lot of special food needs, I don't think a meal service is for you. Anyway, we get our box on Tuesdays and on Monday I receive an email saying my box is on its way and what recipes are in it. That email also tells you what's coming for the next week. You can change your recipes up to a few days ahead, which might be convenient if you are worried about what you are getting. You can also go online and see many weeks out and change any of those too. I will say this though, if you are picky picky and not open minded about trying new recipes, I don't know if you should sign up. Blue Apron's recipes are very unique and have a lot of ethnic flavor profiles and spices and things like that; but they have all been great, again, if you want to have fun and try new things. There have been a couple where we thought maybe we should change that, maybe we won't like it, but we didn't and just went ahead and tried it and we have not regretted it once. You can see more on the review I posted.