try the british chocolate biscuit cake (made of cookies, chocolate, milk, chilled in fridge) or other no-bake cakes (Italian, Irish, American). perfect for this weather.
see, for example:
http://edible-ireland.com/2012/06/21/chocolate-biscuit-cake/
online.wsj.com/article/SB10001424053111904060604576574790327460286.html?mod=WeekendHeader_Rotator
Coconut 'Cheesefake' adapted by Sarah Waybright of WhyFoodWorks.com
From recipes at www.barerootgirl.com & www.bonappetit.com.
http://www.thekitchn.com...

I say crack a window and do a simple but deadly brownie or butterscotch blondie. Carrot cake is a personal favorite of mine but doesn't often go over well with children. If you must, I have a really good no bake cheesecake (which I loved as a child, but I was/am weird), which I set in a sheet pan, cut into squares and top with all sorts of fresh fruit. If you're short on time, "no bake" things often need a length of time to chill and set, so it may be worth a brief period of oven time.

I make wonderful "Black Bottom" Cupcakes. They are a simple chocolate cupcake; before baking you add a spoonful of a cream cheese-chocolate chip mixture that sinks down to the center as it bakes to make a creamy filling. They are moist and delicious, and they only bake 20 minutes. If your interested I can send the recipe if you message me. I don't know if you're able to get cream cheese or chocolate chips, but everyone asks me to bring these...

Thank you for the suggestions. In the end, I will go with the brownies, as the cakes will be outside all afternoon and I am afraid anything containing cream cheese might become bad...