I have a Black Jack cutting that is doing OK. It was molded so I just planted it in a small humidity dome and sat in the window sill. Now it is producing three nice shoots and a few roots. I can either leave it in the window for the sunlight on the new leaves, or place it in a box on a heating mat with bagged cuttings.

Which is better, sunlight for photosynthesis or heat to the roots? I can't do both.

BtW, the box is staying 72-77, and the widow sill is probably 65-68F.

at rooting stage, most important thing is root. i would go for root if i were you. however, if there is enough roots to sustain the leaves, i'll go with sunlight. either way, the young plants will still need some humidity unless your room is humid. it's lot of juggling. 

i have 3 bins. one is for new cuttings in cups. they don't get much light at all. i'm looking for roots. once they have roots and started putting out the leaves, they go into another bin where it will get some sunlight, but heavily filtered. it's not doing much good, but that's the best i can do. if the branches are tall enough and the leaves are getting larger then they go into different bin where more advanced cuttings go into. that bin is usually very humid. cups in that bin, i have to water them since leaves are perspiring water and soil is getting drier quicker. 

Gene,
If its growing OK in the window, just leave it there. Although the optimal temperatures for growth are above 70 Deg F., your temperatures are above 60 deg F so it will continue to grow, just a little bit slower. The sunlight will also aid in the plant growth. I had healthy rooted cuttings growing in a south facing widow in an unheated room with temperature between 45 deg F and 65 deg. F. last year.

Since you have roots, I'd go for sun.  Maybe you can insulate the bottom part of the plant so it stays as warm as possible.

Need light 12 hrs -18 hrs
Root heat will cause the roots to grow. My mat with a thermostat keeps the media and the air 77-81F in the chamber.
You can keep the top of the cutting 10 degrees lower than the roots and that will reduce leaf growth. My air temp outside of the chamber varies 70-75F.
Too much foliage and not enough roots to support them is a problem.
With my humidity chamber and heat mat I get allot of roots before I get leaves.
As soon as I get a bud to open I take it out of the humidity chamber but keep it on the mat.

I'm growing in perlite and I'm watering with hydroponic solution - "dutch bucket" to drain

This week I had one leaf that grew 5x it's size in 7 days. Tiny to half the size of a dollar bill. Crazy.

Sunlight.

I'm not sure how many roots I've got, but I have seen at least one very long one. I think I will put it in the bid, on the heat mat except on sunny days. Then maybe I will get the best of both worlds. By the way, I have it all inside a big double ziplock, so the humidity inside is high.

you don't want humidity to be too high. new bud on tip of the new growth is very tender. if there is too much humidity, they can rot. i would air them out just enought there won't be moisture collecting on them.

I air them out every few days. I probably give them TOO MUCH attention ;-)

everything in moderation. my room has RH of 18%. if the tree stays out long enough, it will dry up the leaves and they will all drop. the roots in cup still can't deliver water fast enough to keep them hydrated. i killed enough cuttings in cup this way. top will completely dry out, and the roots will rot. cutting is done. or it could be other way around.. roots will rot and top will dry. but in the cup, i can see the roots and they were not rot. 

if your room has RH of 60% or so, sure leave it without humidity bin. i heard you can let the new growth to be accumulated to low humidity also. i would rather not chance it. i leave the lid removed on my humidity bin 15-30 min at a time as needed to make sure water doesn't sit on the bud. 

I was surprised that my HCs went straight from sphag bin (well rooted) to un-domed 3quart pots and did great in a rather dry room. I do have a strong tube fluorescent light setup and keep the room in the mid-70s. Can't say if it's just that these cuttings were particularly tenacious or if maybe getting them in heat and good light did the trick. Just thought I'd share that. Seems all my theories of "perfect growth environment" change with each batch/cultivar I root :/  It may be that the larger pot was able to give off enough humidity in the little space around the cutting to make the difference? Personally, I've had bad luck with growing cuttings in <70*F. Seems the cups/pots hold too much moisture for too long when not in a very warm environment. It seems also if you introduce the cuttings to drier air as soon as they leaf out, they will adapt and be fine. Once they've spent too much time in high-humidity, adapting to drier air becomes trickier.