Can I put my brooder outside?

I hope I'm not asking a question that has been covered already, but if anyone knows I'd appreciate your comments.

I have 6 5 week old chicks. 5 are feathered in well, but I have 6th that is lagging behind. She is about 1/2 way feathered. Currently they are in the house, but of course at this point are getting stinky and dusty (I change their bedding frequently, but they're just getting too big). I have them in a brooder made from a little tykes toy chest and I've covered the top with hardware cloth. We have a covered porch that I thought they might do OK in at night. I would keep them in the brooder and secure the top so it can't be opened by a predator (we don't have many, but just in case). I thought if I put the brooder against the house wall it would be protected from the weather. I may also tarp half to give a little more shelter just in case there was rain, etc that managed to get in the porch. Temps have been getting down to low 40s high 30s at night. Coop should be done in the next week...

Thanks for your help.

 

Thanks That's the way I was leaning. We'll see how it goes!