When can the babies go outside?
I would give them another week inside, since that will give you time to check the temperature of the outdoor house at night (if you can borrow a min-max thermometer - those things are great!)
Are you going to cover the openings with half inch metal hardware cloth? They need ventilation, but the half inch metal hardware cloth keeps predators out (when securely installed).
Everything likes to eat duck - that's my mantra when building a shelter.
At 3 weeks of age, they need to be no colder than around (90 minus 3 times 5 is 90 minus 15 is 75) 75 degrees F.
Yes, people put their ducklings out in colder weather, but here is my thought. Ducklings are developing. They only have a certain amount of energy. If they have to spend that energy staying warm to stay alive, they won't have it to build bones, muscles, nerves and organs. I like to give ducklings the best head start that I can.
Just a reminder if you are using a heat lamp - how will you prevent a fire? I am sure you have thought of it, so it would be good to discuss that for people who read this thread later.
Could you describe the mesh? Is it metal, plastic, chicken wire, window screen?
Whatever goes over openings needs to be tough enough that raccoons cannot rip it open. If they can, they will. If they can pull out the staples, they will.
Predators have all night and sometimes all day to rip, claw, tear and dig their way in to get to ducks. Please use that to guide your shelter construction.