My girls are off heat by that age (but I raise them outdoors, so they harden up to the temperatures faster that way). So yes it's safe to take them out, as long as you have a secure place for them to explore, with something to serve as shade & windblock (a box turned on its side works well).
You absolutely can have them moved out in 2-3 weeks provided you get them acclimated to the temperatures, which shouldn't be hard. You can start by turning off the MHP (but you can leave it in for a few more days, so they have the security of having it around, even if it's not heating up) and taking them outside for increasing periods of time.