They are known as The Persian Silk Tree because of their silk like flowers and the leaves are lovely too. Some years ago I was given some seeds to try and grow but didn't have any success. Unlike you, I didn't use a heated propagator, so well done.

I would pot them on into bigger pots as the roots develop and get too big for the pots they're in. They grow quite big and I think they are quite hardy over here, so eventually they need to be planted into the ground in a suitable site for their size.

I don't grow this but have just looked on the web. As Myron says they are supposed to be hardy over here but, seemingly, lose there leaves in winter. As they are a northern hemisphere shrub they would be in there dormant phase now so I would hold off potting on until the end of winter. I would suggest taking them out of the heated propagator and keeping them somewhere cool but frost free for this winter.

I have them - from seed like you. As Bulbaholic says, they are deciduous - mine have already lost most of their leaves. It takes several years for the first flowers to open, and will grow over 3 meters tall with an open habit. At some point, to get the most, you will have to put them in the ground, which I would do in early spring. Since I am not in the UK, I cann't give more advice than this.

I too would remove them from the propagator, as I found that the seedlings dislike the humidity.

I hate to contradict BA as he is one of the wisest members of the forum, but I have yet to here of it being reliably hardy. As such, my 25cm seedlings are in the conservatory and a cold frame (this will be moved if it gets bitter).

If there are any viable seeds left they will germinate without heat, just a lot slower.

It can be a little confusing about their hardiness. I've looked it up and it's mentioned that they are hardy, but delving deeper this seems to refer to cultivars that are sold at garden centres, etc, to grow in colder climates and not the wild ones found in the sub tropics. I don't know if the tree that the seeds came from are the more hardy type, and if it is will they take on the hardy tolerance from the mother tree? I doubt it though as I think that if grown from seed it might revert back.

I just choked on my lunch, Meanie :-)))). There are much wiser GoYers than I am; if I were wise I would learn to keep my mouth shut.
My information on this shrub is entirely from the internet, I had not heard of it before but was interested in macb's question.

You do yourself down sir!

My seed were sent to me by a GoY'er which she had collected on her holiday in the Med as I recall.

The advice regarding humidity came from a member of staff at Oxfords botanic gardens - I popped the question in one day as we talked and hey presto, no lost seedlings!

Originally a deciduous persian/chinese plant? Cold temperate climates are not a problem.

Here in the States, it is known to be hardy down to -29º C, but it will probably need good drainage.